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

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Table Of Integrals Series And Products

We review the current status of our knowledge of the chemical composition of the Sun, essentially derived from the analysis of the solar photospheric spectrum. The comparison of solar and meteoritic abundances confirms that there is a very good agreement between the two sets of abundances. They are used to construct a Standard Abundance Distribution.

Standard Solar Composition

QUANTUM gravitational effects are usually ignored in calculations of the formation and evolution of black holes. The justification for this is that the radius of curvature of space-time outside the event horizon is very large compared to the Planck length (Għ/c3)1/2 ≈ 10−33 cm, the length scale on which quantum fluctuations of the metric are expected to be of order unity. This means that the energy density of particles created by the gravitational field is small compared to the space-time curvature. Even though quantum effects may be small locally, they may still, however, add up to produce a significant effect over the lifetime of the Universe ≈ 1017 s which is very long compared to the Planck time ≈ 10−43 s. The purpose of this letter is to show that this indeed may be the case: it seems that any black hole will create and emit particles such as neutrinos or photons at just the rate that one would expect if the black hole was a body with a temperature of (κ/2π) (ħ/2k) ≈ 10−6 (M/M)K where κ is the surface gravity of the black hole1. As a black hole emits this thermal radiation one would expect it to lose mass. This in turn would increase the surface gravity and so increase the rate of emission. The black hole would therefore have a finite life of the order of 1071 (M/M)−3 s. For a black hole of solar mass this is much longer than the age of the Universe. There might, however, be much smaller black holes which were formed by fluctuations in the early Universe2. Any such black hole of mass less than 1015 g would have evaporated by now. Near the end of its life the rate of emission would be very high and about 1030 erg would be released in the last 0.1 s. This is a fairly small explosion by astronomical standards but it is equivalent to about 1 million 1 Mton hydrogen bombs. It is often said that nothing can escape from a black hole. But in 1974, Stephen Hawking realized that, owing to quantum effects, black holes should emit particles with a thermal distribution of energies — as if the black hole had a temperature inversely proportional to its mass. In addition to putting black-hole thermodynamics on a firmer footing, this discovery led Hawking to postulate 'black hole explosions', as primordial black holes end their lives in an accelerating release of energy.

Black Hole Explosions

Ann. Rev. Astron. Astrophys. 1987. 25: 425-72 Copyright © 1987 by Annual Reviews Inc. All rights reserved EXISTENCE AND NATURE OF DARK MATTER IN THE UNIVERSE Virginia T rimble Astronomy Program, University of Maryland, College Park, Maryland 20742, and Department of Physics, University of California, Irvine, California 92717 1. HISTORICAL INTRODUCTION AND THE SCOPE OF THE PROBLEM The ﬁrst detection of nonluminous matter from its gravitational effects occurred in 1844, when Friedrich Wilhelm Bessel announced that several decades of positional measurements of Sirius and Procyon implied that each was in orbit with an invisible companion of mass comparable to its own. The companions ceased to be invisible in 1862, when Alvan G. Clark turned his newly-ground 18%” objective toward Sirius and resolved the 10q‘ of the photons from the system emitted by the white dwarf Sirius B. Studies of astrometric and single-line spectroscopic binaries are the modern descendants of Bessel’s work. A couple of generations later, data implying nonluminous matter on two very different scales surfaced almost simultaneously. First, Oort (498, 499) analyzed numbers and velocities of stars near the Sun and concluded that visible stars fell shy by 30-50% of adding up to the amount of gravitating matter implied by the velocities. Then, in 1933, Zwicky (777) concluded that the velocity dispersions in rich clusters of galaxies required 10 to 100 times more mass to keep them bound than could be accounted for by the luminous galaxies themselves. The former result was taken much more seriously than the latter by contemporary and succeeding astronomers (being digniﬁed by the name “the Oort limit”), which is perhaps more a statement about the personalities of Oort and Zwicky than about anything else. 425 0066-4146/87/0915—0425$02.00 © Annual Reviews Inc. - Provided by the NASA Astrophysics Data System

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Existence and Nature of Dark Matter in the Universe

A NATO Advanced Studies Institute on the Origins and Abundances of the Chemical Elements was held at the Institute of Astronomy, Cambridge, England from 23 July to 9 August 1974. The problems discussed there are the basis for this review. Three major areas can be identified. First, the normal distribution of chemical and isotopic abundances and deviations from it must be determined observationally. Second, the relevant nuclear processes and their sites and products must be identified. Third, a model of the evolution of galaxies which includes the relevant processes and produces the observed abundances must be formulated. There has been rapid progress recently in all three of these areas. © 1975 American Physical Society.

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The origin and abundances of the chemical elements

Proper motions have been measured for 132 line-emitting filaments in the Crab Nebula on direct plates taken with the 100 and 200-inch telescopes. These motions, if assumed constant and extrapolated backwards in time, converge toward a point about 12" southeast of the double star near the center of the nebula. The filaments approach, on the average, most closely to that point or expansion center in about the year 1140, indicating that the expansion has been somewhat accelerated.

Proper motions and radial velocities were measured for an additional 126 features on the same direct plates and Mt. Wilson and Palomar spectra. These, along with other, nondynamical data, indicate a most probable distance to the object of 2.02 kpc. Two projections of the nebula perpendicular to the one seen in the plane of the sky are constructed and do not differ significantly from that presented to us.

The proper motion and radial velocity of the nebula as a whole are found and converted into galactic coordinates. This requires several assumptions of questionable validity. The nebula seems to be moving about 112 km/sec faster than the galactic rotation at its position. The proper motion of the so-called central star translates into an equally unlikely space motion, but this is also extremely uncertain. The likelihood of a physical connection between the star and the nebula is discussed.

The line-emitting filaments are shown to be distributed throughout the nebula rather than being confined to a thin outer envelope. The motions are largely radial, each filament having a velocity approximately proportional to its distance from the expansion center. The deviations from this proportionality are as large as .032"/yr or 300 km/sec and have mean values near .010"/yr or 70 km/sec. These deviations are correlated with the scatter of the filaments around the expansion center in 1140.

Photographic materials on pp. 99 and 101 are essential and will not reproduce clearly on Xerox copies. Photographic copies should be ordered.

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Motions and structure of the filamentary envelope of the Crab Nebula

We report observations with the Chandra X-ray Observatory of the single, cool, magnetic white dwarf GD 356. For consistent comparison with other X-ray observations of single white dwarfs, we also re-analyzed archival ROSAT data for GD 356 (GJ 1205), G 99-47 (GR 290 = V1201 Ori), GD 90, G 195-19 (EG250 = GJ 339.1), and WD 2316+123 and archival Chandra data for LHS 1038 (GJ 1004) and GD 358 (V777 Her). Our Chandra observation detected no X rays from GD 356, setting the most restrictive upper limit to the X-ray luminosity from any cool white dwarf - Lx less than 6.0 x 10(exp 25) erg s(sup -1), at 99.7% confidence, for a 1- keV thermal-bremsstrahlung spectrum. The corresponding limit to the electron density is no less than 4.4x10(exp 11) per cubic centimeter. Our re-analysis of the archival data confirmed the non-detections reported by the original investigators. We discuss the implications of our and prior observations on models for coronal emission from white dwarfs. For magnetic white dwarfs, we emphasize the more stringent constraints imposed by cyclotron radiation. In addition, we describe (in an appendix) a statistical methodology for detecting a source and for constraining the strength of a source, which applies even when the number of source or background events is small.

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Virginia Trimble

Papers

Existence and Nature of Dark Matter in the Universe

The origin and abundances of the chemical elements

Motions and structure of the filamentary envelope of the Crab Nebula

Motions and structure of the filamentary envelope of the Crab Nebula

A Chandra Search for Coronal X Rays from the Cool White Dwarf GD 356