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

Monthly Notices is one of the three largest general primary astronomical research publications. It is an international journal, published by the Royal Astronomical Society. This article 1 describes its publication policy and practice.

Monthly Notices of the Royal Astronomical Society

This program was supported by the the Kavli Foundation, Danish National Research Foundation, the Niels Bohr International Academy, and the DARK Cosmology Centre. The UCSC group is supported in part by NSF grant AST-1518052, the Gordon & Betty Moore Foundation, the Heising-Simons Foundation, generous donations from many individuals through a UCSC Giving Day grant, and from fellowships from the Alfred P. Sloan Foundation (R.J.F.), the David and Lucile Packard Foundation (R.J.F. and E.R.) and the Niels Bohr Professorship from the DNRF (E.R.). AMB acknowledges support from a UCMEXUS-CONACYT Doctoral Fellowship. Support for this work was provided by NASA through Hubble Fellowship grants HST-HF-51348.001 (B.J.S.) and HST-HF-51373.001 (M.R.D.) awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. This paper includes data gathered with the 1 meter Swope and 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile.r (AGILE) The AGILE Team thanks the ASI management, the technical staff at the ASI Malindi ground station, the technical support team at the ASI Space Science Data Center, and the Fucino AGILE Mission Operation Center. AGILE is an ASI space mission developed with programmatic support by INAF and INFN. We acknowledge partial support through the ASI grant No. I/028/12/2. We also thank INAF, Italian Institute of Astrophysics, and ASI, Italian Space Agency.r (ANTARES) The ANTARES Collaboration acknowledges the financial support of: Centre National de la Recherche Scientifique (CNRS), Commissariat a l'energie atomique et aux energies alternatives (CEA), Commission Europeenne (FEDER fund and Marie Curie Program), Institut Universitaire de France (IUF), IdEx program and UnivEarthS Labex program at Sorbonne Paris Cite (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02), Labex OCEVU (ANR-11-LABX-0060) and the A*MIDEX project (ANR-11-IDEX-0001-02), Region Ile-de-France (DIM-ACAV), Region Alsace (contrat CPER), Region Provence-Alpes-Cite d'Azur, Departement du Var and Ville de La Seyne-sur-Mer, France; Bundesministerium fur Bildung und Forschung (BMBF), Germany; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO), the Netherlands; Council of the President of the Russian Federation for young scientists and leading scientific schools supporting grants, Russia; National Authority for Scientific Research (ANCS), Romania;...

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Multi-messenger Observations of a Binary Neutron Star

This is a redacted transcript of a course given by the author at Harvard in spring semester 2016. It contains a pedagogical overview of recent developments connecting the subjects of soft theorems, the memory effect and asymptotic symmetries in four-dimensional QED, nonabelian gauge theory and gravity with applications to black holes. The lectures may be viewed online at this https URL. Please send typos or corrections to strominger@physics.this http URL.

Lectures on the Infrared Structure of Gravity and Gauge Theory

We explore the prospects of detecting Galactic double white dwarf (DWD) binaries with the space-based gravitational wave (GW) observatory TianQin. In this work, we analyze both a sample of currently known DWDs and a realistic synthetic population of DWDs to assess the number of guaranteed detections and the full capacity of the mission. We find that TianQin can detect 12 out of $\ensuremath{\sim}100$ known DWDs; GW signals of these binaries can be modeled in detail ahead of the mission launch, and therefore they can be used as verification sources. Besides, we estimate that TianQin has a potential to detect as many as ${10}^{4}$ DWDs in the Milky Way. TianQin is expected to measure their orbital periods and amplitudes with accuracies of $\ensuremath{\sim}{10}^{\ensuremath{-}7}$ and $\ensuremath{\sim}0.2$, respectively, and to localize on the sky a large fraction (39%) of the detected population to better than $1\text{ }\text{ }{\mathrm{deg}}^{2}$. We conclude that TianQin has the potential to significantly advance our knowledge on Galactic DWDs by increasing the sample up to 2 orders of magnitude, and will allow their multimessenger studies in combination with electromagnetic telescopes. We also test the possibilities of different configurations of TianQin: (1) the same mission with a different orientation, (2) two perpendicular constellations combined into a network, and (3) the combination of the network with the ESA-led Laser Interferometer Space Antenna. We find that the network of detectors boosts the accuracy on the measurement of source parameters by 1--2 orders of magnitude, with the improvement on sky localization being the most significant.

Science with the TianQin Observatory: Preliminary results on Galactic double white dwarf binaries

TianQin is a space-based laser interferometric gravitational wave detector aimed at detecting gravitational waves at low frequencies (0.1 mHz–1 Hz). It is formed by three identical drag-free spacecrafts in an equilateral triangular constellation orbiting around the Earth. The distance between each pair of spacecrafts is approximately . The spacecrafts are interconnected by infrared laser beams forming up to three Michelson-type interferometers. The detailed mission design and the study of science objectives for the TianQin project depend crucially on the orbit and the response of the detector. In this paper, we provide the analytic expressions for the coordinates of the orbit for each spacecraft in the heliocentric-ecliptic coordinate system to the leading orders. This enables a sufficiently accurate study of science objectives and data analysis, and serves as a first step to further orbit design and optimization. We calculate the response of a single Michelson detector to plane gravitational waves in arbitrary waveform which is valid in the full range of the sensitive frequencies. It is then used to generate the more realistic sensitivity curve of TianQin. We apply this model on a reference white-dwarf binary as a proof of principle.

https://iopscience.iop.org/article/10.1088/1361-6382/aab52f/pdf

Fundamentals of the orbit and response for TianQin

We study the capability of the space-based gravitational wave observatory TianQin to test the no-hair theorem of general relativity, using the ringdown signal from the coalescence of massive black hole binaries. We parametrize the ringdown signal by the four strongest quasinormal modes and estimate the signal to noise ratio for various source parameters. We consider constraints both from single detections and from all the events combined throughout the lifetime of the observatory, for different astrophysical models. We find that at the end of the mission, TianQin will have constrained deviations of the frequency and decay time of the dominant 22 mode from the general relativistic predictions to within 0.2% and 1.5% respectively, the frequencies of the subleading modes can be also constrained within 0.3%. We also find that TianQin and LISA are highly complementary, by virtue of their different frequency windows. Indeed, LISA can best perform ringdown tests for black hole masses in excess of $\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{6}\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$, while TianQin is best suited for lower masses.

Science with the TianQin observatory: Preliminary results on testing the no-hair theorem with ringdown signals

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Science prospects for space-borne gravitational-wave missions

TianQin is a space-based laser interferometric gravitational wave detector aimed at detecting gravitational waves at low frequencies (0.1 mHz -- 1 Hz). It is formed by three identical drag-free spacecrafts in an equilateral triangular constellation orbiting around the Earth. The distance between each pair of spacecrafts is approximately $1.7 \times 10^{5} ~\rm{km}$. The spacecrafts are interconnected by infrared laser beams forming up to three Michelson-type interferometers. The detailed mission design and the study of science objectives for the TianQin project depend crucially on the orbit and the response of the detector. In this paper, we provide the analytic expressions for the coordinates of the orbit for each spacecraft in the heliocentric-ecliptic coordinate system to the leading orders. This enables a sufficiently accurate study of science objectives and data analysis, and serves as a first step to further orbit design and optimization. We calculate the response of a single Michelson detector to plane gravitational waves in arbitrary waveform which is valid in the full range of the sensitive frequencies. It is then used to generate the more realistic sensitivity curve of TianQin. We apply this model on a reference white-dwarf binary as a proof of principle.

Jianwei Mei

Papers

Science with the TianQin Observatory: Preliminary results on Galactic double white dwarf binaries

Fundamentals of the orbit and response for TianQin

Science with the TianQin observatory: Preliminary results on testing the no-hair theorem with ringdown signals

Science prospects for space-borne gravitational-wave missions

Fundamentals of the orbit and response for TianQin