Gravitational Waves

Great excitement about the opening of a new era in the observation of the universe has been generated by the first detection of gravitational waves by the LIGO interferometers on September 14, 2015 at 5:51 a.m. Eastern Daylight Time. This image posted on the Cal Tech site will undoubtedly be an icon for the new field of observation.

These are plots of the signals received by the two LIGO interferometers at Hanford, Washington and Livingston, Louisiana. The two signals were in excellent agreement but separated in time, reaching Hanford 0.007 seconds after detection in Livingston. Corresponding to a distance difference of about 2000 km at the speed of light, this is consistent with the idea that the exchange particle, the graviton, associated with gravity is massless and therefore the gravity wave travels at the speed of light.

Image Courtesy Caltech/MIT/LIGO Laboratory

If an analogy with sound waves were used to describe the signals shown above, you might describe it as a "chirp" since the frequency starts out low and increases until its termination. The initial model of the source of this signal is that of two black holes of masses about 29 and 36 solar masses orbiting each other until they coalesce into a single black hole of mass about 62 solar masses. This would correspond to the conversion of about 3 solar masses into energy during this brief event, described on the Caltech site as having a "peak power output about 50 times that of the whole visible universe".

Although the projected distance has large error bars, the most probable distance is about 1.3 x 109 light years.

References:
Cal Tech, image of data

Caltech news release, February 11, 2016

LIGO Educator's Guide

Einstein and Gravity Waves
Events leading to observed signal
Comments on the model data from this event
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Einstein and Gravity Waves

This is a brief description of gravity waves from the LIGO Educator's Guide : "Gravitational waves are 'ripples' in the fabric of spacetime caused by accelerating masses such as colliding black holes, exploding stars, and even the birth of the universe itself. Albert Einstein predicted the existence of gravitational waves in 1916, derived from his General Theory of Relativity. Einstein's mathematics showed that massive accelerating objects would disrupt spacetime in such a way that waves of distorted space would radiate from the source. These ripples travel at the speed of light through the universe, carrying information about their origins, as well as clues to the nature of gravity itself.

Two black holes in mutual orbit will revolve around each other emitting gravitational waves and losing orbital energy as illustrated at right. Over time, the energy loss causes the stars to move closer together and orbit around each other faster and faster until they eventually merge together, or coalesce. This type of merger has never before been directly observed, and it is the type of event that emitted the gravitational waves detected by LIGO on September 14, 2015.

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Events Leading to Observed Gravity Wave Signal

These descriptive images from the LIGO Educator's Guide depict models of the events leading to the LIGO observations of gravity waves on September 14, 2015.


Artist's depiction of the merger process of two black holes, accompanied by the actual waveforms detected by LIGO Hanford and Livingston detectors. Credit: SSU E/PO Aurore Simonnet

GW150914 models. Credit: LIGO

The gravitational waves for two coalescing black holes was compared to the gravitational wave signal from LIGO and was found to be very similar.

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Comments on the Model of the Gravity Wave Event

The model of the observed gravitational wave event suggests the coalescing of two black holes of masses 29 and 36 solar masses. The Schwarzschild radii of such black holes would be about 86km and 106km respectively. Before coalescing into one black hole, they were orbiting each other in a binary orbit which can be modeled based on the period of rotation.
The times between the centers of the last few peaks were scaled as shown. The Science News article says that in the 0.2 seconds before the coalition of the two bodies the frequency increased from 17 to 75 revolutions per second.

The model suggests that the final black hole is about 62 solar masses, so that 3 solar masses were converted to energy in the gravitational waves. Considering that about 1 gram of mass conversion powered the Hiroshima bomb, this is hard to visualize. The team's comparison was to suggest that the power was over 50 times the total light output of the universe.

The 0.007 second interval between the detection of the gravitational waves at Livingston and Hanford is quite significant. That corresponds to about 2100 km at the speed of light, so correlates well with the presumption that gravity waves made up of gravitons travel at the speed of light, being massless.

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