Gravity Waves

UC Connect: Black holes making waves around the Universe

Professor David Wiltshire, Department of Physics and Astronomy
Monday, March 7, 2016 from 7:30 PM – 8:45 PM
C1 Lecture Theatre, University of Canterbury

On 14 September 2015 the two LIGO detectors measured gravitational waves for the first time ever, produced by the collision of two black holes 1.3 billion light years away. This opens a new era of astronomy, a window on things we cannot observe by other means. It vindicates Einstein’s 100 year old prediction of gravitational waves, and the rotating black hole solution of Einstein’s equations discovered in 1963 by New Zealander Roy Kerr.

In measuring distance changes a thousandth the size of a proton, this is also the most sensitive measurement ever achieved by humankind. It represents the culmination of four decades of work by thousands of experimental physicists, engineers, mathematicians, numerical modellers and astronomers, who together have had to overcome challenges in fields as diverse as seismology and fundamental quantum optics. Last December, the LISA pathfinder satellite was launched, the first step in taking gravitational wave detection to space. This lecture will reflect on what has been achieved, the technological spin-offs and challenges ahead, and what we might discover in the new age of astronomy ahead.

Notes from wikipedia:
Gravitational waves are presently understood to be described by Albert Einstein’s theory of general relativity. In the simplest cases, and certain less-dynamic situations, the energy implications of gravitational waves can be deduced from other conservation laws such as those governing conservation of energy or conservation of momentum.

On 11 February 2016, the LIGO collaboration announced the detection of gravitational waves, from a signal of two black holes with masses of 29 and 36 solar masses merging together about 1.3 billion light years away.

During the final fraction of a second of the merge, it released more power than 50 times that of all the stars in the observable universe combined. The signal increases in frequency from 35 to 250 Hz as it rises in strength. The mass of the new black hole obtained from merging the two was 62 solar masses. Energy equivalent to three solar masses (our sun is 1 solar mass, 2×10^30 Kg) was emitted as gravitational waves in about 1/10 of a second. The signal was seen by both LIGO detectors, in Livingston and Hanford, with a time difference of 7 milliseconds due to the angle between the two detectors and the source. The signal came from the Southern Celestial Hemisphere, in the rough direction of (but much further away than) the Magellanic Clouds. The confidence level of this being an observation of gravitational waves was 99.99994%.

Amplitude: Usually denoted h, this is the size of the wave — the fraction of stretching or squeezing in the animation.
Gravitational waves passing through the Earth are about 10^−20m.

Wave amplitudes from the Earth–Sun system
We can also think in terms of the amplitude of the wave from a system in circular orbits.
Suppose that an observer is outside the system at a distance 0.08 Light Years (7.5 x 10^14m) from its center of mass. Typical amplitudes will be h ≈ 10^−25m. This is well under the detectability limit of all conceivable detectors.

Power radiated by orbiting bodies
Two stars of dissimilar mass are in circular orbits. Each revolves about their common center of mass (denoted by the small red cross) in a circle with the larger mass having the smaller orbit.
Two stars of similar mass are in circular orbits about their center of mass

Gravitational waves carry energy away from their sources and, in the case of orbiting bodies, this is associated with an inspiral or decrease in orbit.  Imagine for example a simple system of two masses — such as the Earth–Sun system — moving slowly compared to the speed of light in circular orbits. Assume that these two masses orbit each other in a circular orbit in the x–y plane. To a good approximation, the masses follow simple Keplerian orbits. However, such an orbit represents a changing quadrupole moment. That is, the system will give off gravitational waves.

In theory, the loss of energy through gravitational radiation could eventually drop the Earth into the Sun. However, the total energy of the Earth orbiting the Sun (kinetic energy + gravitational potential energy) is about 1.14×10^36 joules of which only 200 joules per second is lost through gravitational radiation, leading to a decay in the orbit by about 1×10^−15 meters per day or roughly the diameter of a proton. At this rate, it would take the Earth approximately 1×10^13 times more than the current age of the Universe to spiral onto the Sun.

In Fiction: An episode of the Russian science-fiction novel Space Apprentice by Arkady and Boris Strugatsky shows the experiment monitoring the propagation of gravitational waves at the expense of annihilating a chunk of 15 Eunomia the size of Everest. The novel was written in 1961 and published in 1962, exactly at the time when Soviet physicists Michail Gerstenstein and Vladislav Pustovoit prepared and published their proposal on using laser interferometry for gravitational wave detection.