gravitational waves: sources and...

Anthony Alberti 1

Physics 105 Mark Kruse

Gravitational Waves: Sources and Detection

Artist’s rendition of LISA

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Einstein’s theory of general relativity describes the force of gravity as the physical

warping of spacetime. While the field equations can be used to describe the gravitational field

created by a static object, they should also describe what happens to spacetime when matter is

moving. Like a buoy bobbing in a body of water, a massive object in motion should produce

gravitational waves. Since the travelling waves are space and time, they should distort matter

that exists in space and time as they pass by it. Since general relativity is accepted as the best

theory of gravity, and that gravitational waves are a result of the theory, it is accepted in theory

that gravitational waves exist. However, the changes to spacetime that would be caused here on

Earth are extremely minute, so many laboratories have been built to detect them. Scientists have

already worked out the theoretical response on the laboratories to numerous astrophysical

phenomena, such as supernovae, asymmetric rotating neutron stars, and colliding black holes.

(Greene 419-23)

Many astronomical objects can radiate gravitational waves, but it depends on the type of

motion and the symmetry of the object or system. For example, a spinning spherically-symmetric

mass cannot emit gravitational waves because gravitational potential a given distance away is not

changing. Similarly, if the mass were to expand or contract symmetrically, this would also not

produce waves. A cylindrically-symmetric mass spinning on its rotationally-symmetric axis will

not emit gravitational waves, though if it rotates on a different axis through the center of mass, it

will. Similarly, a binary system releases waves; even though it rotates around its center of mass

(which can be used as an approximate location of the combined mass from far distances), the

potential changes as the two masses rotate. (Exception: gravitational waves would not be

detected on the axis of rotation for a binary system of two equally massive objects, though this is

from destructive interference.) This gravitational radiation of the system releases energy just as

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electromagnetic radiation would, and the theory can show how the distance between the two

objects decreases over time, called inspiral. Binary systems may also emit gravitational waves

from their collapse. For neutron star-neutron star and neutron star-black hole systems, the

deformation of neutron stars should emit more readily detectable gamma-ray bursts; if the light is

detected, the laboratories can see if gravitational waves were detected as well. For black hole-

black hole systems, the most gravitational radiation should be emitted during the collision and

during ringdown, where the new, asymmetric black hole will radiate its perturbations as

gravitational waves and become a rotating, spherically symmetrical black hole. (Jaranowski 26-

28, Goggin 709)

Another rotational source of gravitational waves is an asymmetric neutron star; for

example, a neutron star’s magnetic field can be misaligned with its rotational axis, causing the

star to warp in directions perpendicular to the rotational axis. Supernovae could be prime

examples of large gravitational bursts (assuming most supernovae are not spherically

symmetric), though due to are lack of understanding of the progression of a supernova and the

various types of emissions, it is harder to predict what the gravitational radiation will look like.

The radiation from undetected supernovae could be lumped into stochastic sources, which

include a background of gravitational activity that could be other undetected astrophysical

sources or possibly cosmic strings. It is also possible that, much like the Cosmic Microwave

Background, the stochastic sources include an early-universe gravitational wave background.

(Jaranowski 28-30)

The direct effects of a passing gravitational wave would be the stretching and

compressing of matter. This is very difficult to detect because sources of large waves are very far

away, and closer systems do not emit enough energy. For example, the gravitational energy

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radiated by the Earth orbiting the Sun is only 200 Joules per second. More energetic events are

happening so far away, that the part of the wave that would reach the Earth is greatly dissipated.

Brian Greene gives the example of a supernova 10,000 lightyears away (the shape of the

supernova is not specified, so perhaps he is taking a reasonable percentage of the total energy of

the system). A powerful wave created that far away would only stretch 1 meter by 10-18

meter.

(Greene 419-20)

One indirect method of testing the existence of gravitational waves, explored by Russell

Hulse and Joseph Taylor, is measuring the increasing rotational frequency of a binary system

with a pulsar. The pulsar’s periodic emission of light makes it reliable to measure and track its

rotational motion. Hulse and Taylor monitored a binary pulsar system from 1974 on and have

found that the increasing rotational frequency matches the prediction of general relativity within

half a percent. This is strong indirect evidence, but the Hulse-Taylor system is too far away to

measure waves directly. Closer binary systems have been discovered since, and huge laboratories

have been built to directly observe the changes in distance. (Greene 531)

The original devices for detecting gravitational waves were theorized and built by Joseph

Weber. These were called resonant bars, massive metal bars that could resonate to the

frequencies of passing waves. The bars had to be read by sensors able to detect vibrations of less

than 10-18

m, but this could be easily interfered with by thermal vibrations; hence, the bars were

cooled to a fraction above absolute zero. Many other types of interference hamper the data from

resonant bars, and currently only two laboratories still use resonant bars for detection. The bars

may be useful for detecting low-frequency waves, but they would have to be very powerful to

register detection (Blair 43-47, Collins 8-13)

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The most highly examined gravitational wave detection devices today are laser

interferometers. These laboratories are composed of two arms that meet at a 90 degree and are

very large; the arms of TAMA 300 at the National Astronomical Observatory of Japan in Tokyo

are 300 m long, GEO 600 in Sarstedt, Germany is likewise 600 m long, and Virgo at the

European Gravitational Observatory in Cascina, Italy is 3 km long. The Laser Interferometer

Gravitational-Wave Observatory (LIGO), two American laboratories, is the longest on Earth

with 4 km-long arms at Livingston, Louisiana and the Hanford Nuclear Reservation in

Washington. The Hanford laboratory also houses a half-size interferometer at 2 km. LIGO uses a

Michelson interferometer, which splits a beam of light to mirrors, or free masses. The beams

bounce back and register together in a photodiode; they are tuned so that in total “silence” (no

interference, gravitational or otherwise) the beams will completely destructively interfere,

registering no light. If Earth-bound conditions are ideal, a passing gravitational wave will distort

the length of the arms. The amount and type of distortion depends on the angle of approach to

the detector and the polarization of the wave. Gravitational waves are polarized because of the

regular motion of their sources (though a supernova could release a complicated combination of

polarizations); unlike light, they are polarized “plus,” h+, or 45 degrees skewed “cross,” h×. The

warping in either polarization causes stretching in one direction perpendicular to wave

propagation and compression perpendicular to the stretching and propagation. Hence, while a

gravitational wave could propagate along a line on the detector’s plane of symmetry and be

polarized so that it causes equal changes in length, the ideal wave direction and polarization for

detection would be through the plane of the detector polarized parallel to the arms, which would

cause maximum stretching along one arm and maximum contraction along the other. This would

put the lasers out of destructive phase (though this is not necessarily where the data is collected).

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To increase the effectiveness of LIGO, the lasers are made to bounce back and forth in the arms

about 75 times, increasing the distance of light traveled to 300 km, increasing the sensitivity of

detection at the photodiode. The Laser Interferometer Space Antenna (LISA) is also being

planned by NASA and the European Space Agency to orbit around the Sun with three arms in an

equilateral triangle, 5 million km long. (Blair 12-14, 269-70, Greene 420-21, Collins 13-16)

Image 2: The northern arm of LIGO at Hanford, Washington

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The basics of the theory behind the gravitational waves show how the different

polarizations affect different directions of space. The metric for a wave propagating in the

positive-z direction is: ��, ��

0 00 �� 0 0��

�� 00 ��

��0 0 �� 00 0�

��

Notice how the matrix is not diagonal. While the diagonal components are inverses, which

makes sense because h+ distorts in the x and y directions, one stretching and one compressing,

the off-diagonal components account for the skewed h× polarization and introduce a complex

line element:

�� 1 � �� !� � �1 � ��

�� "� � 2�� !�" � �$�

Again, the changes from static space are opposite for h+, and more readily gleaned from the line

element because the distortions are along the Cartesian axes. The h× changes are not as easy to

describe, but it is also interesting that the wave causes no distortions in the direction in the

direction it is propagating. (Jaranowski 12, 116)

Even LIGO can only detect changes up to 10-18

m and is given a “range” radius of up to

15 Megaparsecs. The range of a detector is measured to its ability to detect a binary system of

two 1.4M☉ stars (from an averaged detectable direction). LIGO and Virgo are installing new

technology to increase this range, named “advanced LIGO” (adLIGO) and “advanced Virgo”,

and LIGO operated on an in-between “enhanced LIGO” (eLIGO) for a year. eLIGO hopes to

have double the range of the “initial LIGO” (iLIGO), which increases the spherical volume of

detection by a factor of 8, a considerable increase in detectable galaxies, and thus star systems

that emit gravitational radiation. adLIGO hopes to have a range of more than 10 times iLIGO, a

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volume more than 1000 times larger. For all of these detectors, though, unwanted interference

can significantly diminish the detection range. (Collins 15-16)

Considering the extreme sensitivity required to detect these faint gravitational waves, the

laboratories attempt to block as many extraneous effects as possible. The lasers pass through

vacuum chambers that are controlled for various kinds of interference, such as electromagnetic

radiation. The mirrors are suspended by pendulums and springs with automated force-feedback,

so the many terrestrial vibrations (planes flying low, trucks driving by, seismic activity) are

directly countered, keeping the split beam in “lock,” on focus on the diode. This feedback

mechanism would also respond to the desired detection of gravitational waves, hence the data is

collected and analyzed from how the feedback responds. The LIGO project can adjust for many

unwanted vibrations because the two laboratories are far apart on the Earth, and because of the

transparency of Earth to gravitational waves, if a vibration is detected in one LIGO of an

expected gravitational-wave frequency that is not detected in the other, it can be ruled out. Still,

coincidences can still occur, so scientists work with a coincidence background determined by

“time-shifting” the data of one interferometer and summing what are then truly coincidental

vibrations. If the possible vibration would be in the detectable range of the smaller

interferometers, the data from them are also checked. (Collins 16-20, Greene 421-22)

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Image 3: Basics of an interferometer. The test masses are mirrors that reflect the light multiple

times to increase photodetection sensitivity. The mirrors are suspended with automated-feedback

devices to keep the mirrors from moving and collect movement data.

Even with the feedback system, larger terrestrial vibrations can move the mirrors,

throwing the lasers out of “lock” and rendering those periods of data collection useless. Even in

“lock” the feedback can be active enough to overshadow delicate gravitational radiation (even

with dedicated detectors of the terrestrial vibrations for awareness), and some of the non-

gravitational wave vibrations may be unidentifiable. For LIGO, the detection mechanisms

determine when the conditions are good for data collection and declare “science mode,” but

during science mode the device can also administer data-quality flags for potentially corrupted

data. The scientists then examine the flagged data and can choose to veto it outright, consider it

in light of surrounding good data of interest, or just use it to help determine an upper limit when

searching through data. With all this to work around, iLIGO’s fifth and most sensitive run lasted

for two years but only yielded one year of continuous usable data. (Collins 16-20)

Bernard F. Schutz outlines multiple data processing techniques to increase the chances of

finding a true signal. For burst sources like supernovae, he describes a high deviation threshold

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to distinguish from typical Gaussian and white noise. This threshold falls as you compare data

from multiple detectors for coincidences, though if the detectors are not at the same site (which

is true for interferometers except the two at Hanford), it goes up slightly to account for time-

delay false coincidences, or noise data that could look like a signal if it occurs in the right

timeframe between separate detectors. For regular binary system signals, the waves will not stick

out from the noise like a supernova, but the periodic signal can be extracted by matching it with

known theoretical predictions; hence, the detection range for binary systems is actually larger

than for momentary events that do not have the same theoretical explanation. Fourier analysis

would have to be applied to the data to detect periodic signals, and Schutz describes how to

account for white noise (which affects all frequencies) and seismic activity (which enforces a

low-frequency cutoff). If the laboratory wants to claim detection of a binary source, it will also

need to determine the time the signal arrived, which can also be altered by noise. Sampling rates

and other technical adjustments are also discussed, and analyzing all the data may take a great

amount of computing power. LIGO seems to have responded by helping to develop

Einstein@Home, a distributed computing software that anyone with a computer and Internet

access can download to donate some of their computer’s processing time. (Blair 406-26)

As of this writing, gravitational waves have not been directly detected. The data from

LIGO is still being examined, and the Einstein@Home has helped, so far having discovered two

binary pulsar systems. Still, with only a year’s worth of data from LIGO most fine-tuned run,

scientists are hoping that increasing reliability of the detectors, thereby increasing the range, will

demonstrate repeated detections, rather than relying on what could be an isolated detection in

iLIGO’s data. NASA hopes to launch LISA in 2025, which will be able to detect low-frequency

gravitational waves. Even with an arm length of 5*109 m, it can only detect changes of 2*10

-11

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m, giving it about the same resolution as LIGO, about 1 to 120

, but because it will not experience

violent terrestrial disturbances, it will respond better to gradual, long-wavelength changes that

could be buried by unwanted interference in Earth’s detectors. Sources of low-frequency waves

include small, compact bodies being engulfed by supermassive black holes at the center of

galaxies and binary systems not yet approaching coalescence. Part of the difference with LIGO is

that scientists know to look for a “chirp,” or rising-frequency signal, when a binary system is

speeding up and approaching collision. LISA hopes to detect the more regular wave radiation

from these binary systems before they coalesce.

The excitement in finding gravitational waves is largely due to how scientists could apply them

to examine the universe. Scientists have been using light waves of low and high frequency to

examine matter that interacts with light, but physicists have also theorized the existence of

“dark” matter that does not interact with light. Perhaps if gravitational waves could be created

and manipulated, the existence and properties of dark matter could be evaluated, since gravity

interacts with all matter. Also, light may be obscured by opaque materials or by dominating

sources of light (such as the bright center of our galaxy). Gravity is such a weaker force that it

could penetrate obstructing matter and give access to previously hidden parts of the universe.

Successfully identifying a gravitational-wave background, like the CMB, could also give new

insight into cosmology. Between working out theoretical expectations from more and more

potential sources, refining and expanding detection laboratories, and improving data analysis, all

the scientific parts are working together to make the likely existence and application of

gravitational waves realizable. (Greene 22-23)

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Works Cited

Allen, B. (2011). Einstein@Home. Retrieved April 25, 2011, from

http://einstein.phys.uwm.edu/

Blair, D. G. (1991). The Detection of Gravitational Waves. Cambridge: Cambridge UP.

Collins, H. (2011). Gravity's Ghost: Scientific Discovery in the Twenty-first Century. Chicago:

University of Chicago Press.

Goggin, L. M. (2006). Search for Black Hole Ringdown Signals in LIGO S4 Data [Electronic

Version]. Classical and Quantum Gravity, 23, 709-713, from

http://www.ligo.caltech.edu/docs/P/P060085-00.pdf

Greene, B. (2004). The Fabric of the Cosmos. New York: Vintage Books.

Jaranowski, P., & Krolak, A. (2009). Analysis of Gravitational-Wave Data. Cambridge:

Cambridge UP.

Vallisneri, M. (2011, April 10). LISA - Laser Interferometer Space Antenna. Retrieved April

25, 2011, from http://lisa.jpl.nasa.gov/index.html

Picture Credits

Title page: taken from LISA website (see citation above)

Image 2: taken from Wikimedia Commons

Image 3: taken from Wikimedia Commons

gravitational waves: sources and...

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