Gravitational waves
N. K. Johnson-McDaniel
TPI, FSU Jena
Wintersemester 2013
What are gravitational waves (GWs)?
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Intuitively, “ripples in spacetime” that carry energy and
(angular) momentum away from an isolated source; the
gravitational analogue of electromagnetic radiation, so
sourced by accelerated masses. (We’ll see the more rigorous
version later.)
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But, unlike E&M radiation, extremely weak. While one can
generate GWs by literally waving one’s hands, that radiation
would be completely undetectable (as would any gravitational
radiation one can conceive of being generated in the solar
system). This is why we don’t feel like we are swimming in
molasses from gravitational radiation reaction when we move
around.
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GWs of any appreciable magnitude can only be generated by
astronomical objects, primarily compact objects like neutron
stars and black holes (and white dwarfs, though these are not
nearly so compact).
Other important qualitative properties of GWs and
detectors
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Despite extremely close formal analogies with E&M radiation,
GWs are often more like sound (acoustic radiation) than
electromagnetic radiation.
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In particular, since they are generated by bulk motion of the
source, they generally have wavelengths of about the size of
the source or larger, and thus can’t be used to form an image.
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They are phase-coherent, unlike most E&M radiation, so we
can directly observe the field (as opposed to some sort of
energy), which only falls off as 1/r , instead of 1/r 2 . Thus, if
we double our detector’s sensitivity, we increase its reach by
nearly an order of magnitude! (23 = 8)
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Gravitational wave detectors are naturally all-sky monitors,
unlike most astronomical observatories, which have to work to
increase their field of view.
See Sec. 6 in Flanagan and Hughes for more detailed discussion.
Why an entire course on GWs?
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These days, mostly because of experiment and astrophysics.
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There are multimillion dollar international collaborations
devoted to detecting gravitational waves (e.g.,
LIGO/Virgo/KAGRA/IndIGO and LISA [eLISA/NGO]).
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...and ever since observations of the Hulse-Taylor pulsar
indirectly demonstrated the existence of GWs, they have been
a staple of descriptions of the evolution of compact
binaries—and even, lately, galactic dynamics (through the
“kicks” that can be generated by merging black hole binaries).
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But on the more theoretical/mathematical side, the question
of whether gravitational waves even exist in GR (and if they
really carry away energy and angular momentum from the
source), and how to characterize them has motivated many
advances in our understanding of general relativity, as you will
hear about from David.
Why? (cont.)
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Returning to observation, while the direct detection of
gravitational waves will provide all sorts of interesting tests of
fundamental gravitational physics (by probing strong-field
gravity, as well as just detecting the waves themselves),
gravitational waves are also a powerful tool for astrophysics,
from studying compact objects, to such bread-and-butter
astrophysics as star formation, binary evolution, and galactic
mergers.
In particular, since GWs tell us what is going on with the bulk
motions of mass, they would let us probe the supernova (SN)
mechanism (E&M observations only observe the surface, and
even neutrinos take a little while to diffuse out).
They’ll also generally help us learn more about cold matter at
supernuclear densities, from observations of neutron stars.
Additionally, since GWs interact so weakly, like neutrinos, we
can observe them from sources (e.g., some SNe and white
dwarf binaries in our own galaxy) that are completely
obscured by dust and thus unobservable electromagnetically.
Why? (cont.)
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Of course, since GWs are so weak, the signals one is trying to
detect are almost always hidden in the noise, so one needs
highly accurate templates to detect the signals, and—in
particular—to extract the properties of the source from the
signal. Building such templates has driven much theoretical
work over the past few decades.
This course will present the basics of GWs, give elementary
tools for computations of the waves emitted by a source, and
then discuss the detection of these waves (and the sources
expected for current and planned detectors), and how to infer
properties of the source from them.
And while the “flagship” strong-field sources (most notably
coalescing compact binaries) require exquisitely accurate
templates generated by exacting analytical and numerical
work, the tools we develop will be perfectly adequate to
describe other, equally important (if perhaps not quite so
glamorous) sources.
Why? (cont.)
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We will focus on the GR side of things (with a little statistics
at the end). However, one needs pretty much all of physics to
describe the standard GW sources. Even for binary black
holes, that paradigmatic vacuum GR system, one needs lots of
nuclear physics and radiation hydrodynamics to describe the
stars that explode to create stellar mass black holes, in
addition to much laser physics for the detectors.
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Indeed, to quote my Ph.D. advisor:
My main research interest is the detection of gravitational
waves. People call this relativity, but I wind up doing most of
physics except relativity. —B. J. Owen
GW detectors: From the ground...
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Since GWs are so weak, one requires a huge detector to
observe them [plus lots of tough experimental work to reduce
(and characterize) the noise].
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On the ground, there are currently the two LIGO detectors in
the US, the Virgo detector in Italy, and the GEO600 detector
in Hannover. All these detectors use the principle of laser
interferometry.
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Even with the LIGO detectors’ 4 km arms, the maximal
changes in armlength that can be expected from a GW are
∼ 4 × 10−18 m, well below the nuclear scale (10−15 m)!
LIGO Hanford, 4 km
Virgo (Pisa), 3 km
GEO600 (Hannover), 600 m
GW detectors: ...to Earth orbit...
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LISA
Due to seismic noise, one cannot go below ∼ 1 Hz with
ground-based GW detectors (and the current detectors do not
go below 10 Hz, even with upgrades). Thus, to access the
rich mHz regime, including GWs from galactic binaries and
coalescing supermassive black hole binaries, one needs to go
into space.
The LISA mission was the standard space-based GW detector
design for many years, but recently has been downscaled to an
ESA-only mission (eLISA/NGO), with a somewhat shorter
armlength (likely 106 km vs. the original 5 × 106 km). It will
be preceded by the technology demonstration mission LISA
Pathfinder.
LISA Pathfinder
GW detectors: ...and throughout the galaxy
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One can also search for low-frequency (nHz) GWs (from, e.g.,
ultramassive black hole binaries with periods of ∼ 1 year)
using radio observations of pulsars (generally at distances of
100s of pc)—one looks for correlated changes in arrival time
of the pulses from many pulsars in different directions, which
could only be caused by a gravitational wave.
However, unlike all the other GW detectors, pulsar timing only
observes sources that are moving slowly enough that most
relativistic effects will be unobservable.
Schematic of pulsar timing from the Manchester group.
GW detector status
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LIGO and Virgo are currently being upgraded to “Advanced”
sensitivity (about an order of magnitude
improvement)—expected to be operational in 2014.
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They will be joined later by other, similar ground-based
detectors in Japan (KAGRA, formerly LCGT) and India
(IndIGO) somewhat later (∼ 2017) to make a world-wide
network of detectors, around the time first detections are
expected with the “Advanced” instruments (based on models
for the population of sources).
GW detector status (cont.)
Timeline from the IndIGO website.
GW detector status (cont.)
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eLISA/NGO’s funding status is still not confirmed, though the
optimistic timeline has it launch in 2028, and it is still possible
that the original LISA design could be resurrected (with
contributions from NASA or some other agency). Regardless,
LISA Pathfinder is slated to fly in 2015.
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ET, DECIGO, BBO, etc. are even further in the future.
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Pulsar timing is taking data now, and only improving in
sensitivity (and baseline). (There’ll be a dramatic
improvement in sensitivity when the Square Kilometre Array
comes online in 2020.)
The GW spectrum and various detectors
[Figure from T. Creighton’s website]
Converting from wavelength to the more common representation in terms of frequency, note that
λ = {1027 , 1016 , 1011 , 109 , 106 , 103 } m ⇒ f = {3 × 10−19 Hz, 30 nHz, 3 mHz, 0.3 Hz, 300 Hz, 300 kHz}
An illustration of the GW data analysis challenge
Example of some realistic compact binary signals hidden in
ground-based detector noise from the companion to PRD 88,
062001 (2013).
(With LISA, there’s the possibility of being able to pick out the brightest SMBHB signals in the data by eye,
though there are other data analysis challenges for LISA...)
What has GW science already achieved?
While there have not yet been any direct GW detections, LIGO
and Virgo have set some interesting upper limits at their initial and
“Enhanced” sensitivities.
GRBs and SGRs
In particular, they showed that two gamma-ray
bursts (GRBs) whose sky positions were
coincident with (relatively) nearby galaxies (M31
[the Andromeda Galaxy], our sister galaxy, and
M81) were not produced by (quasicircular)
compact binary coalescences in those galaxies.
They are thought most likely to come from soft
gamma repeater (SGR) flares if they indeed
originated in those galaxies.
Error box for potential GRB
(SGR flares are thought to be caused by a large-scale rearrangement of the magnetic
in M31.
field of a magnetar, a highly magnetized neutron star with a field strength of
∼ 1015 G.)
What has GW science already achieved? (cont.)
Deformations of pulsars
They also constrained the contribution of gravitational waves to
the Crab pulsar’s spin-down power (the amount of rotational
energy it has to lose to account for the observed increase in its
period) to be . 1%. Alternatively, they have constrained its
quadrupole ellipticity to be . 10−4 , a factor of ∼ 10 below the
limit placed by electromagnetic observations of the spin-down.
This corresponds to a surface deformation of ∼ 5–30 cm (EOS-dependent) on a star with a radius of ∼ 10 km (!).
Cas A NS and nebula, Chandra
Crab pulsar and nebula, Chandra
(LIGO and Virgo have also placed similar, though less stringent, direct constraints for other pulsars, notably the
Vela pulsar and the Cas A central object. However, for most pulsars, the constraints from the electromagnetically
observed spin-down are still well below the direct GW constraints.)
Conclusions
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As we have seen briefly here and will explore in the rest of the
course, GW observations promise to be a powerful tool for
both astrophysics and fundamental physics, giving one views
of the universe and strong gravity that are inaccessible with
any other messenger (photons, cosmic rays, or neutrinos),
perhaps most notably with supernovae and compact object
binaries (plus—if we are very fortunate—the early universe).
Gravitational waves also are an important driving force in
compact binary evolution, in that they are what finally drives
the binary to coalescence (while efficiently circularizing the
orbit); such coalescence of binaries containing neutron stars is
thought to lead to GRBs. The neutron-rich ejecta from these
mergers also enriches the interstellar medium with heavy
r-process elements.
Also, in certain circumstances, the GW emission during merger
can impart a substantial “kick” to the binary, even enough to
eject it from its host galaxy in extreme cases. (This is a teaser for later!)
Conclusions (cont.)
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However, the experimental challenge in making the first direct
detections of GWs is immense. We will not touch on most of
the issues here, though we will discuss the very basics of
detector design and data analysis. In particular, we will show
how one is able to estimate the accuracy with which GW
detectors will be able to measure the parameters of various
sources.