- Email: [email protected]
Gravitational-wave physics
Nuclear Physics B (Proc. Suppl.) 138 (2005) 429–432 www.elsevierphysics.com
Gravitational-wave physics S.A. Hughes∗ a a
Department of Physics and Center for Space Research Massachusetts Institute of Technology Cambridge, MA 02139
A new generation of interferometric gravitational-wave (GW) detectors has begun operations. They are rapidly approaching a level of sensitivity such that direct detection of GWs is possible (though not quite probable). A vigorous program of R&D and planned upgrades promises to improve sensitivity to the level that detection is very probable, converting these detectors into astrophysical observatories. In this talk, I give an overview of GW science, describing the basic physics of GWs and motivating their promise for astrophysics.
1. BACKGROUND A common misconception outside the community of GW researchers is that the primary purpose of observatories such as LIGO is to directly detect GWs. Although the first unambiguous direct detection will certainly be a celebrated event, the real excitement will come when GW detection can be used as an observational tool for astronomy. GW science is currently in a state analogous to neutrino science circa 1950: we have a mature theoretical framework describing GWs; we have compelling indirect evidence for their existence; but unambiguous direct detection has not yet happened. In contrast to neutrinos, the only guaranteed sources of GWs bright enough to be measurable will arise from violent astrophysical events. Though frustrating on the one hand — we must remain patient while we wait for nature to supply events — it offers great opportunity on the other. GWs promise to open a unique window onto astrophysical phenomena that may teach us much about “dark” processes in the universe. The properties of GWs and the processes driving their emission are quite different from those of electromagnetic (EM) radiation: • EM radiation typically comes from the incoherent superposition of photons from many emitters ∗ This
work supported by NASA Grant NAG5-12906 and NSF Grant PHY-0244424. I thank Kip Thorne for permission to use Fig. 1. This article was adapted from portions of Refs. [9,10].
0920-5632/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2004.11.098
(e.g., electrons in the solar corona, hot plasma in the early universe). This probes directly the thermodynamic state of a system or an environment. GWs are coherent superpositions arising from the bulk dynamics of a dense mass-energy source. This probes directly a system’s dynamics. • The direct GW observable is the waveform h, a quantity that falls off as 1/r. EM observables are usually related to an energy flux, and so they fall off as 1/r 2 . Small improvements in GW sensitivity can have a large science impact: doubling sensitivity doubles the detectable distance, increasing measurable volume by a factor of 8. Every factor of 2 improvement in GW sensitivity should increase the number of measurable sources by about an order of magnitude. • EM waves interact strongly with matter; GWs do not. This is both a blessing and a curse, meaning that GWs propagate to observers with essentially no absorption, making it possible to probe astrophysics that is hidden or dark, e.g., the coalescence and merger of black holes, the collapse of a stellar core, the dynamics of the early universe, but also meaning that the waves interact very weakly with detectors. • The wavelength of EM radiation is typically smaller than the emitting system, and so it can be used for source imaging. By contrast, GW wavelengths are comparable to or larger than their source size, so GWs cannot be used for imaging. Instead, GWs are analogous to sound. The two polarizations carry a stereophonic description of
430
S.A. Hughes / Nuclear Physics B (Proc. Suppl.) 138 (2005) 429–432
the source’s dynamics. • Much astronomy is based on deep imaging of small fields of view; we gain a large amount of information about a small piece of the sky. GW astronomy, by contrast, will be a nearly all-sky affair; the detectors have nearly 4π steradian sensitivity. A consequence is that their ability to localize a source on the sky is not so good, but any source can in principle be detected, not just sources towards which the detector is “pointed”. The contrast between the all-sky sensitivity, but poor resolution of GW observatories, versus the pointed, high resolution of telescopes is very similar to the resolution contrast of hearing and sight, strengthening the analogy of GWs with sound. 2. OVERVIEW OF GW PHYSICS GWs are a consequence of general relativity, described as a tensor perturbation to the metric of spacetime propagating at the speed of light, and with two independent polarizations. As EM waves come from the acceleration of charges, GWs are generated by the acceleration of masses. At lowest order, GWs come from the time-changing quadrupole moment of mass and energy. Monopole waves would violate massenergy conservation, dipole waves violate momentum conservation. GWs act by changing the distance between widely separated objects. Because they arise from quadrupolar oscillations, they are themselves quadrupolar, squeezing along one axis while stretching along the other, i.e., acting tidally. GW detectors measure this tidal field by measuring the change in distance between widely separated masses. Typically, the masses are laid out in an “L” shape to take advantage of the alternate stretching and squeezing along orthogonal axes. Fig. 1 shows a sketch of a GW interferometer. General relativity tells us a GW changes the difference in the length of the two arms as follows: δL(t) ≡ L1 (t) − L2 (t) = h(t)L .
(1)
(In the absence of a wave, L1 L2 = L.) The GW acts as a strain in the detector; h is often called the “wave strain”. The wave must fall off with distance as 1/r to
Figure 1. Layout of a GW interferometer (from Ref. [1]).
conserve the total energy flowing through large spheres. The lowest order contribution comes from the source’s time-changing quadrupole moment, Q. To order of magnitude, Q ∼ (source mass)(source size)2 . Dimensional analysis then tells us h∼
¨ GQ . c4 r
(2)
¨ 2M v2 We can further approximate this by Q ns ns 4Ekin ; v is the source’s internal velocity, and Ekin is the nonspherical part of its internal kinetic energy. GW sources have strong non-spherical dynamics, e.g., compact binaries, stellar core collapse, dynamics of the early universe. For an interesting event rate, we must be sensitive to sources at rather large distances. For example, to measure binary neutron star coalescence, we should reach out ∼ 100 Megans parsecs (Mpc) [2–5]. For this source, Ekin /c2 ∼ 1 solar mass. Plugging this and r ∼ 100 Mpc into Eq. (2) yields h ∼ 10−21 − 10−22 .
(3)
This sets the sensitivity required to measure GWs. Using Eq. (1), we see that for every kilometer of baseline L, we must measure a shift δL ∼ 10−16 cm! Such measurement is possible with laser interferometry [6]. Each arm in Fig. 1 is a Fabry-Perot cavity, tuned such that each photon bounces
S.A. Hughes / Nuclear Physics B (Proc. Suppl.) 138 (2005) 429–432
roughly 100 times before exiting. The accumulated phase shift during those bounces is ∆ΦGW ∼ 100 × 2 × ∆L × 2π/λ ∼ 10−9 .
(4)
This shift can be measured provided that the shot √ noise, ∆Φshot ∼ 1/ N , is less than ∆ΦGW . N is the number of √photons accumulated over the measurement; 1/ N is the magnitude of phase fluctuation in a coherent state. We therefore must accumulate ∼ 1018 photons over the roughly 0.01 second measurement, translating to a laser power of about 100 watts. In fact, one can use a much less powerful laser [7]. Even in the presence of a GW, only a tiny bit of the exiting light goes to the photodiode; the vast majority is sent back to the laser. A recycling mirror bounces this light back into the arms. This mirror is labeled “R” in Fig. 1. A laser of ∼ 10 watts drives several hundred watts to circulate in the “recycling cavity”, and ∼ 10 kilowatts in the arms. Thermal excitations are overcome by averaging over many vibrations. For example, the atoms on the mirror surface oscillate with amplitude kT δlatom = ∼ 10−10 cm, (5) mω2 at temperature T , with m atomic mass and with frequency ω ∼ 1014 s−1 . This is huge relative to the GW’s effect — how can we possibly measure the wave? The answer is that these vibrations are random and incoherent. The ∼ 7 cm wide laser averages over ∼ 1017 atoms and ∼ 1011 vibrations in a typical measurement. These vibrations are irrelevant compared to the coherent GW. Other thermal vibrations are not irrelevant and dominate the noise in certain frequency bands. For example, the masses’ normal modes are thermally excited. They vibrate at ω ∼ 105 s−1 and have mass m ∼ 10 kg, so δlmass ∼ 10−14 cm, much larger than the GW’s effect. However, the modes are very high frequency, and can be averaged away provided the test mass has a high-quality factor Q. Understanding noise in GW detectors is an active field of current research; see, e.g., other contributions in this session. The fundamental fact to keep in mind is that a GW acts coherently on the relevant length and time scales, whereas noise acts incoherently.
431
3. ASTROPHYSICS Sources are discussed in depth by other speakers in this session. Here, we outline some particularly interesting ones: • Early universe. Metric fluctuations from the Big Bang are amplified by inflation, producing a broad-band spectrum. Even optimistically, this will be far too weak to be detected in the near future. Phase transitions or brane-world effects may produce a stochastic spectrum strong enough to be measured (cf. [9], Secs. 3.2.2, 4.4, and 5.4). • Core collapse. The collapse of stellar cores in supernovae should be a strong source of GWs, though theoretical uncertainties are very large. See talk by C. Cardall. • Neutron star vibrations. “Bumps” and fluid instabilities in neutron stars can produce interesting GW strains. Particularly promising are waves from accreting neutron stars [8]. Such waves may be used to study neutron star properties and nuclear material; see talk by K. Kokkotas. • Coalescing binaries. Our current best data on GWs comes from binary neutron star systems [5]. Mature GW detectors (cf. talk by D. Sigg) are expected to see many events from these sources. See [9], Sec. 3.2.1 and 5.1 for further discussion. More detail on these sources is in the review articles [9,10] and references therein. Note that there is great promise for coordinated observations with other forms of radiation — cf. S. M´ arka’s talk on GWs and “multimessenger” astronomy. REFERENCES 1. A. Abramovici et al., Science 256 325 (1992). 2. R. Narayan, T. Piran, and A. Shemi, Astrophys. J. 379 (1991) L17. 3. E. S. Phinney, Astrophys. J. 380 (1991) L17. 4. V. Kalogera and D.R. Lorimer, Astrophys. J. 530 (2000) 890. 5. M. Burgay et al., Nature 426 (2003) 531. 6. R. Weiss, Quarterly Progress Report of RLE, MIT 105 (1972) 54. 7. R.W.P. Drever, in Gravitational Radiation, N. Deruelle and T. Piran (eds.), North Holland, Amsterdam, 1983.
432
S.A. Hughes / Nuclear Physics B (Proc. Suppl.) 138 (2005) 429–432
8. D. Chakrabarty et al., Nature 424 (2003) 42. 9. S.A. Hughes, S.M´ arka, P.L. Bender, and C.J. Hogan, in Proceedings of the APS / DPF / DPB Summer Study on the Future of Particle Physics (Snowmass 2001), R. Davidson and C. Quigg, (eds.), eConf C010630, p. 402 (2001). 10. S.A. Hughes, Ann. Phys. 303 (2003) 142.
Gravitational-wave physics S.A. Hughes∗ a a
Department of Physics and Center for Space Research Massachusetts Institute of Technology Cambridge, MA 02139
A new generation of interferometric gravitational-wave (GW) detectors has begun operations. They are rapidly approaching a level of sensitivity such that direct detection of GWs is possible (though not quite probable). A vigorous program of R&D and planned upgrades promises to improve sensitivity to the level that detection is very probable, converting these detectors into astrophysical observatories. In this talk, I give an overview of GW science, describing the basic physics of GWs and motivating their promise for astrophysics.
1. BACKGROUND A common misconception outside the community of GW researchers is that the primary purpose of observatories such as LIGO is to directly detect GWs. Although the first unambiguous direct detection will certainly be a celebrated event, the real excitement will come when GW detection can be used as an observational tool for astronomy. GW science is currently in a state analogous to neutrino science circa 1950: we have a mature theoretical framework describing GWs; we have compelling indirect evidence for their existence; but unambiguous direct detection has not yet happened. In contrast to neutrinos, the only guaranteed sources of GWs bright enough to be measurable will arise from violent astrophysical events. Though frustrating on the one hand — we must remain patient while we wait for nature to supply events — it offers great opportunity on the other. GWs promise to open a unique window onto astrophysical phenomena that may teach us much about “dark” processes in the universe. The properties of GWs and the processes driving their emission are quite different from those of electromagnetic (EM) radiation: • EM radiation typically comes from the incoherent superposition of photons from many emitters ∗ This
work supported by NASA Grant NAG5-12906 and NSF Grant PHY-0244424. I thank Kip Thorne for permission to use Fig. 1. This article was adapted from portions of Refs. [9,10].
0920-5632/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2004.11.098
(e.g., electrons in the solar corona, hot plasma in the early universe). This probes directly the thermodynamic state of a system or an environment. GWs are coherent superpositions arising from the bulk dynamics of a dense mass-energy source. This probes directly a system’s dynamics. • The direct GW observable is the waveform h, a quantity that falls off as 1/r. EM observables are usually related to an energy flux, and so they fall off as 1/r 2 . Small improvements in GW sensitivity can have a large science impact: doubling sensitivity doubles the detectable distance, increasing measurable volume by a factor of 8. Every factor of 2 improvement in GW sensitivity should increase the number of measurable sources by about an order of magnitude. • EM waves interact strongly with matter; GWs do not. This is both a blessing and a curse, meaning that GWs propagate to observers with essentially no absorption, making it possible to probe astrophysics that is hidden or dark, e.g., the coalescence and merger of black holes, the collapse of a stellar core, the dynamics of the early universe, but also meaning that the waves interact very weakly with detectors. • The wavelength of EM radiation is typically smaller than the emitting system, and so it can be used for source imaging. By contrast, GW wavelengths are comparable to or larger than their source size, so GWs cannot be used for imaging. Instead, GWs are analogous to sound. The two polarizations carry a stereophonic description of
430
S.A. Hughes / Nuclear Physics B (Proc. Suppl.) 138 (2005) 429–432
the source’s dynamics. • Much astronomy is based on deep imaging of small fields of view; we gain a large amount of information about a small piece of the sky. GW astronomy, by contrast, will be a nearly all-sky affair; the detectors have nearly 4π steradian sensitivity. A consequence is that their ability to localize a source on the sky is not so good, but any source can in principle be detected, not just sources towards which the detector is “pointed”. The contrast between the all-sky sensitivity, but poor resolution of GW observatories, versus the pointed, high resolution of telescopes is very similar to the resolution contrast of hearing and sight, strengthening the analogy of GWs with sound. 2. OVERVIEW OF GW PHYSICS GWs are a consequence of general relativity, described as a tensor perturbation to the metric of spacetime propagating at the speed of light, and with two independent polarizations. As EM waves come from the acceleration of charges, GWs are generated by the acceleration of masses. At lowest order, GWs come from the time-changing quadrupole moment of mass and energy. Monopole waves would violate massenergy conservation, dipole waves violate momentum conservation. GWs act by changing the distance between widely separated objects. Because they arise from quadrupolar oscillations, they are themselves quadrupolar, squeezing along one axis while stretching along the other, i.e., acting tidally. GW detectors measure this tidal field by measuring the change in distance between widely separated masses. Typically, the masses are laid out in an “L” shape to take advantage of the alternate stretching and squeezing along orthogonal axes. Fig. 1 shows a sketch of a GW interferometer. General relativity tells us a GW changes the difference in the length of the two arms as follows: δL(t) ≡ L1 (t) − L2 (t) = h(t)L .
(1)
(In the absence of a wave, L1 L2 = L.) The GW acts as a strain in the detector; h is often called the “wave strain”. The wave must fall off with distance as 1/r to
Figure 1. Layout of a GW interferometer (from Ref. [1]).
conserve the total energy flowing through large spheres. The lowest order contribution comes from the source’s time-changing quadrupole moment, Q. To order of magnitude, Q ∼ (source mass)(source size)2 . Dimensional analysis then tells us h∼
¨ GQ . c4 r
(2)
¨ 2M v2 We can further approximate this by Q ns ns 4Ekin ; v is the source’s internal velocity, and Ekin is the nonspherical part of its internal kinetic energy. GW sources have strong non-spherical dynamics, e.g., compact binaries, stellar core collapse, dynamics of the early universe. For an interesting event rate, we must be sensitive to sources at rather large distances. For example, to measure binary neutron star coalescence, we should reach out ∼ 100 Megans parsecs (Mpc) [2–5]. For this source, Ekin /c2 ∼ 1 solar mass. Plugging this and r ∼ 100 Mpc into Eq. (2) yields h ∼ 10−21 − 10−22 .
(3)
This sets the sensitivity required to measure GWs. Using Eq. (1), we see that for every kilometer of baseline L, we must measure a shift δL ∼ 10−16 cm! Such measurement is possible with laser interferometry [6]. Each arm in Fig. 1 is a Fabry-Perot cavity, tuned such that each photon bounces
S.A. Hughes / Nuclear Physics B (Proc. Suppl.) 138 (2005) 429–432
roughly 100 times before exiting. The accumulated phase shift during those bounces is ∆ΦGW ∼ 100 × 2 × ∆L × 2π/λ ∼ 10−9 .
(4)
This shift can be measured provided that the shot √ noise, ∆Φshot ∼ 1/ N , is less than ∆ΦGW . N is the number of √photons accumulated over the measurement; 1/ N is the magnitude of phase fluctuation in a coherent state. We therefore must accumulate ∼ 1018 photons over the roughly 0.01 second measurement, translating to a laser power of about 100 watts. In fact, one can use a much less powerful laser [7]. Even in the presence of a GW, only a tiny bit of the exiting light goes to the photodiode; the vast majority is sent back to the laser. A recycling mirror bounces this light back into the arms. This mirror is labeled “R” in Fig. 1. A laser of ∼ 10 watts drives several hundred watts to circulate in the “recycling cavity”, and ∼ 10 kilowatts in the arms. Thermal excitations are overcome by averaging over many vibrations. For example, the atoms on the mirror surface oscillate with amplitude kT δlatom = ∼ 10−10 cm, (5) mω2 at temperature T , with m atomic mass and with frequency ω ∼ 1014 s−1 . This is huge relative to the GW’s effect — how can we possibly measure the wave? The answer is that these vibrations are random and incoherent. The ∼ 7 cm wide laser averages over ∼ 1017 atoms and ∼ 1011 vibrations in a typical measurement. These vibrations are irrelevant compared to the coherent GW. Other thermal vibrations are not irrelevant and dominate the noise in certain frequency bands. For example, the masses’ normal modes are thermally excited. They vibrate at ω ∼ 105 s−1 and have mass m ∼ 10 kg, so δlmass ∼ 10−14 cm, much larger than the GW’s effect. However, the modes are very high frequency, and can be averaged away provided the test mass has a high-quality factor Q. Understanding noise in GW detectors is an active field of current research; see, e.g., other contributions in this session. The fundamental fact to keep in mind is that a GW acts coherently on the relevant length and time scales, whereas noise acts incoherently.
431
3. ASTROPHYSICS Sources are discussed in depth by other speakers in this session. Here, we outline some particularly interesting ones: • Early universe. Metric fluctuations from the Big Bang are amplified by inflation, producing a broad-band spectrum. Even optimistically, this will be far too weak to be detected in the near future. Phase transitions or brane-world effects may produce a stochastic spectrum strong enough to be measured (cf. [9], Secs. 3.2.2, 4.4, and 5.4). • Core collapse. The collapse of stellar cores in supernovae should be a strong source of GWs, though theoretical uncertainties are very large. See talk by C. Cardall. • Neutron star vibrations. “Bumps” and fluid instabilities in neutron stars can produce interesting GW strains. Particularly promising are waves from accreting neutron stars [8]. Such waves may be used to study neutron star properties and nuclear material; see talk by K. Kokkotas. • Coalescing binaries. Our current best data on GWs comes from binary neutron star systems [5]. Mature GW detectors (cf. talk by D. Sigg) are expected to see many events from these sources. See [9], Sec. 3.2.1 and 5.1 for further discussion. More detail on these sources is in the review articles [9,10] and references therein. Note that there is great promise for coordinated observations with other forms of radiation — cf. S. M´ arka’s talk on GWs and “multimessenger” astronomy. REFERENCES 1. A. Abramovici et al., Science 256 325 (1992). 2. R. Narayan, T. Piran, and A. Shemi, Astrophys. J. 379 (1991) L17. 3. E. S. Phinney, Astrophys. J. 380 (1991) L17. 4. V. Kalogera and D.R. Lorimer, Astrophys. J. 530 (2000) 890. 5. M. Burgay et al., Nature 426 (2003) 531. 6. R. Weiss, Quarterly Progress Report of RLE, MIT 105 (1972) 54. 7. R.W.P. Drever, in Gravitational Radiation, N. Deruelle and T. Piran (eds.), North Holland, Amsterdam, 1983.
432
S.A. Hughes / Nuclear Physics B (Proc. Suppl.) 138 (2005) 429–432
8. D. Chakrabarty et al., Nature 424 (2003) 42. 9. S.A. Hughes, S.M´ arka, P.L. Bender, and C.J. Hogan, in Proceedings of the APS / DPF / DPB Summer Study on the Future of Particle Physics (Snowmass 2001), R. Davidson and C. Quigg, (eds.), eConf C010630, p. 402 (2001). 10. S.A. Hughes, Ann. Phys. 303 (2003) 142.