There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

The first observational run of the Advanced LIGO detectors, from September 12, 2015 to January 19, 2016, saw the first detections of gravitational waves from binary black hole mergers. In this paper we present full results from a search for binary black hole merger signals with total masses up to 100M⊙ and detailed implications from our observations of these systems. Our search, based on general-relativistic models of gravitational wave signals from binary black hole systems, unambiguously identified two signals, GW150914 and GW151226, with a significance of greater than 5σ over the observing period. It also identified a third possible signal, LVT151012, with substantially lower significance, which has a 87% probability of being of astrophysical origin. We provide detailed estimates of the parameters of the observed systems. Both GW150914 and GW151226 provide an unprecedented opportunity to study the two-body motion of a compact-object binary in the large velocity, highly nonlinear regime. We do not observe any deviations from general relativity, and place improved empirical bounds on several high-order post-Newtonian coefficients. From our observations we infer stellar-mass binary black hole merger rates lying in the range 9−240Gpc−3yr−1. These observations are beginning to inform astrophysical predictions of binary black hole formation rates, and indicate that future observing runs of the Advanced detector network will yield many more gravitational wave detections.

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Binary Black Hole Mergers in the First Advanced LIGO Observing Run

Observations of a quasar at redshift 7.54, when the Universe was just five per cent of its current age, suggest that the Universe was significantly neutral at this epoch. Despite extensive searches, only one quasar has been known at redshifts greater than 7, at 7.09. Eduardo Banados and colleagues report observations of a quasar at a redshift of 7.54, when the Universe was just 690 million years old, with a black-hole mass 800 million times the mass of the Sun. The spectrum shows that the quasar's Lyman α emission is being substantially absorbed by an intergalactic medium containing significantly neutral hydrogen, indicating that reionization was not complete at that epoch. Quasars are the most luminous non-transient objects known and as a result they enable studies of the Universe at the earliest cosmic epochs. Despite extensive efforts, however, the quasar ULAS J1120 + 0641 at redshift z = 7.09 has remained the only one known at z > 7 for more than half a decade1. Here we report observations of the quasar ULAS J134208.10 + 092838.61 (hereafter J1342 + 0928) at redshift z = 7.54. This quasar has a bolometric luminosity of 4 × 1013 times the luminosity of the Sun and a black-hole mass of 8 × 108 solar masses. The existence of this supermassive black hole when the Universe was only 690 million years old—just five per cent of its current age—reinforces models of early black-hole growth that allow black holes with initial masses of more than about 104 solar masses2,3 or episodic hyper-Eddington accretion4,5. We see strong evidence of absorption of the spectrum of the quasar redwards of the Lyman α emission line (the Gunn–Peterson damping wing), as would be expected if a significant amount (more than 10 per cent) of the hydrogen in the intergalactic medium surrounding J1342 + 0928 is neutral. We derive such a significant fraction of neutral hydrogen, although the exact fraction depends on the modelling. However, even in our most conservative analysis we find a fraction of more than 0.33 (0.11) at 68 per cent (95 per cent) probability, indicating that we are probing well within the reionization epoch of the Universe.

An 800-million-solar-mass black hole in a significantly neutral Universe at a redshift of 7.5

A theoretical analysis examines the possibility that the gravitational wave signal (GW150914) detected by LIGO was due to the coalescence of primordial black holes created by the extremely dense matter present in the early Universe.

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Primordial Black Hole Scenario for the Gravitational-Wave Event GW150914

We perform population synthesis simulations for Population III (Pop III) coalescing binary neutron stars (NS-NSs), neutron star - black hole binaries (NS-BHs), and binary black holes (BH-BHs) which merge within the age of the universe. We found that the typical mass of Pop III BH-BHs is $\sim 30\ \rm{M}_{\odot}$ so that the inspiral chirp signal of gravitational waves can be detected up to z=0.28 by KAGRA, Adv. LIGO, Adv. Virgo and GEO network. Our simulations suggest that the detection rate of the coalescing Pop III BH-BHs is $140 (68) \cdot ({\rm SFR}_{\rm p}/10^{-2.5} \rm{M}_{\odot} {\rm yr}^{-1} {\rm Mpc}^{-3}) \cdot {\rm Err}_{\rm sys} ~{\rm events} ~{\rm yr}^{-1}$ for the flat (Salpeter) initial mass function (IMF), respectively, where $\rm SFR_p$ and $\rm Err_{sys}$ are the peak value of the Pop III star formation rate and the possible systematic errors due to the assumptions in Pop III population synthesis, respectively. $\rm Err_{sys}=1$ correspond to conventional parameters for Pop I stars. From the observation of the chirp signal of the coalescing Pop III BH-BHs, we can determine both the mass and the redshift of the binary for the cosmological parameters determined by Planck satellite. Our simulations suggest that the cumulative redshift distribution of the coalescing Pop III BH-BHs depends almost only on the cosmological parameters. We might be able to confirm the existence of Pop III massive stars of mass $\sim 30~\rm M_{\odot}$ by the detections of gravitational waves if the merger rate of the Pop III massive BH-BHs dominates that of Pop I BH-BHs.

Possible indirect confirmation of the existence of Pop III massive stars by gravitational wave

Supermassive stars (SMSs) forming via very rapid mass accretion () could be precursors of supermassive black holes observed beyond a redshift of about six. Extending our previous work, here we study the evolution of primordial stars growing under such rapid mass accretion until the stellar mass reaches 104 ? 5 M ?. Our stellar evolution calculations show that a star becomes supermassive while passing through the supergiant protostar stage, whereby the star has a very bloated envelope and a contracting inner core. The stellar radius increases monotonically with the stellar mass until 100?AU for M * 104 M ?, after which the star begins to slowly contract. Because of the large radius, the effective temperature is always less than 104?K during rapid accretion. The accreting material is thus almost completely transparent to the stellar radiation. Only for M * 105 M ? can stellar UV feedback operate and disturb the mass accretion flow. We also examine the pulsation stability of accreting SMSs, showing that the pulsation-driven mass loss does not prevent stellar mass growth. Observational signatures of bloated SMSs should be detectable with future observational facilities such as the James Webb Space Telescope. Our results predict that an inner core of the accreting SMS should suffer from the general relativistic instability soon after the stellar mass exceeds 105 M ?. An extremely massive black hole should form after the collapse of the inner core.

Formation of Primordial Supermassive Stars by Rapid Mass Accretion

We study very-high rate spherically symmetric accretion flows onto a massive black hole (BH; 10 2 . MBH . 10 6 M⊙) embedded in a dense gas cloud with a low abundance of metals, performing one-dimensional hydrodynamical simulations which include multi-frequency radiation transfer and non-equilibrium primordial chemistry. We find that rapid gas supply from the Bondi radius at a hyper-Eddington rate can occur without being impeded by radiation feedback when (n∞/10 5 cm −3 ) > (MBH/10 4 M⊙) −1 (T∞/10 4 K) 3/2 , where n∞ and T∞ are the density and temperature of ambient gas outside of the Bondi radius. The resulting accretion rate in this regime is steady, and larger than 3000 times the Eddington rate. At lower Bondi rates, the accretion is episodic due to radiative feedback and the average rate is limited below the Eddington rate. For the hyper-Eddington case, the steady solution consists of two parts: a radiation-dominated central core, where photon trapping due to electron scattering is important, and an accreting envelope which follows a Bondi profile with T ≃ 8000 K. When the emergent luminosity is limited below the Eddington luminosity because of photon trapping, radiation from the central region does not affect the gas dynamics at larger scales. We apply our result to the rapid formation of massive BHs in protogalaxies with a virial temperature of Tvir & 10 4 K. Once a seed BH forms at the center of the galaxy, it can grow up to a maximum ∼ 10 5 (Tvir/10 4 K) M⊙ via gas accretion independent of the initial BH mass. Finally, we discuss possible observational signatures of rapidly accreting BHs with/without allowance for dust. We suggest that these systems could explain Lyα emitters without X-rays and luminous infrared sources with hot dust emission, respectively.

Hyper-Eddington accretion flows on to massive black holes

The existence of $\approx$10^9 Msun supermassive black holes (SMBHs) within the first billion year of the universe has stimulated numerous ideas for the prompt formation and rapid growth of BHs in the early universe. Here we review ways in which the seeds of massive BHs may have first assembled, how they may have subsequently grown as massive as $\approx$10^9 Msun, and how multi-messenger observations could distinguish between different SMBH assembly scenarios. We conclude the following: (1) The ultra-rare $\approx$10^9 Msun SMBHs represent only the tip of the iceberg. Early BHs likely fill a continuum from stellar-mass (approx. 10 Msun) to the super-massive ($\approx$10^9 Msun) regime, reflecting a range of initial masses and growth histories. (2) Stellar-mass BHs were likely left behind by the first generation of stars at redshifts as high as z=30, but their initial growth was typically stunted due to the shallow potential wells of their host galaxies. (3) Conditions in some larger, metal-poor galaxies soon became conducive to the rapid formation and growth of massive `seed' holes, via gas accretion and by mergers in dense stellar clusters. (4) BH masses depend on the environment (such as the number and properties of nearby radiation sources and the local baryonic streaming velocity), and on the metal enrichment and assembly history of the host galaxy. (5) Distinguishing between assembly mechanisms will be difficult, but a combination of observations by LISA (probing massive BH growth via mergers) and by deep multi-wavelength electromagnetic observations (probing growth via gas accretion) is particularly promising.

The Assembly of the First Massive Black Holes

The existence of ∼109M⊙ supermassive black holes (SMBHs) within the first billion years of the Universe has stimulated numerous ideas for the prompt formation and rapid growth of black holes (BHs) ...

Kohei Inayoshi

Papers

Possible indirect confirmation of the existence of Pop III massive stars by gravitational wave

Formation of Primordial Supermassive Stars by Rapid Mass Accretion

Hyper-Eddington accretion flows on to massive black holes

The Assembly of the First Massive Black Holes

The Assembly of the First Massive Black Holes