Abstract
We study for the first time a three-dimensional octahedron constellation for a space-based gravitational wave detector, which we call the octahedral gravitational observatory (OGO). With six spacecraft the constellation is able to remove laser frequency noise and acceleration disturbances from the gravitational wave signal without needing LISA-like drag-free control, thereby simplifying the payloads and placing less stringent demands on the thrusters. We generalize LISA’s time-delay interferometry to displacement noise free interferometry (DFI) by deriving a set of generators for those combinations of the data streams that cancel laser and acceleration noise. However, the three-dimensional configuration makes orbit selection complicated. So far, only a halo orbit near the Lagrangian point L1 has been found to be stable enough, and this allows only short arms up to 1400 km. We derive the sensitivity curve of OGO with this arm length, resulting in a peak sensitivity of about \(2\times 10^{-23}\,\) Hz \({}^{-1/2}\) near 100 Hz. We compare this version of OGO to the present generation of ground-based detectors and to some future detectors. We also investigate the scientific potentials of such a detector, which include observing gravitational waves from compact binary coalescences, the stochastic background, and pulsars as well as the possibility to test alternative theories of gravity. We find a mediocre performance level for this short arm length detector, between those of initial and advanced ground-based detectors. Thus, actually building a space-based detector of this specific configuration does not seem very efficient. However, when alternative orbits that allow for longer detector arms can be found, a detector with much improved science output could be constructed using the octahedron configuration and DFI solutions demonstrated in this chapter. Also, since the sensitivity of a DFI detector is limited mainly by shot noise, we discuss how the overall sensitivity could be improved by using advanced technologies that reduce this particular noise source.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
G.M. Harry, LIGO Scientific Collaboration, Advanced LIGO: the next generation of gravitational wave detectors. Class. Quantum Gravity 27, 084006 (2010)
The Virgo Collaboration, Advanced Virgo baseline design, VIRC027AC09 (2009). https://tds.ego-gw.it/itf/tds/file.php?callFile=VIR-0027A-09.pdf
J. Abadie et al., [LIGO Scientific and Virgo Collaborations], Predictions for the rates of compact binary coalescences observable by ground-based gravitational-wave detectors. Class. Quantum Gravity 27, 173001 (2010). arXiv:1003.2480
C.L. Fryer, K.C.B. New, Gravitational waves from gravitational collapse. Living Rev. Relat. 14, 1 (2011). http://www.livingreviews.org/lrr-2011-1
B. Owen, Probing neutron stars with gravitational waves, LIGO-T0900053 (2009). arXiv:0903.2603
B. Allen, J.D. Romano, Detecting a stochastic background of gravitational radiation: sensitivities. Phys. Rev. D 59, 102001 (1999). arXiv:gr-qc/9710117
M. Maggiore, Gravitational wave experiments and early universe cosmology. Phys. Rep. 331, 283 (2000). arXiv:gr-qc/9909001
K. Danzmann, The LISA Study Team, LISA - an ESA cornerstone mission for the detection and observation of gravitational waves. Adv. Space Res. 32, 12331242 (2003)
P. Amaro-Seoane et al., eLISA: astrophysics and cosmology in the millihertz regime. GW Notes 6, 4–110 (2013). arXiv:1201.3621
M. Ando et al., DECIGO and DECIGO pathfinder. Class. Quantum Gravity 27, 084010 (2010)
Y. Chen et al., Interferometers for displacement-noise-free gravitational-wave detection. Phys. Rev. Lett. 97, 151103 (2006). arXiv:gr-qc/0603054
S. Kawamura, Y. Chen, Displacement-noise-free gravitational-wave detection. Phys. Rev. Lett. 93, 211103 (2004). arXiv:gr-qc/0405093
Y. Chen, S. Kawamura, Displacement- and timing-noise free gravitational-wave detection. Phys. Rev. Lett. 96, 231102 (2006). arXiv:gr-qc/0504108
M. Tinto, S.V. Dhurandhar, Time-delay interferometry. Living Rev. Relat. 8, 4 (2005). arXiv:gr-qc/0409034, http://www.livingreviews.org/lrr-2005-4
M. Otto, G. Heinzel, K. Danzmann, TDI and clock noise removal for the split interferometry configuration of LISA. Class. Quantum Gravity 29, 205003 (2012)
G. Gomez, A. Jorba, J. Masdemont, C. Simo, Study of the transfer from the Earth to a halo orbit around the equilibrium point L1. Celest. Mech. Dyn. Astron. 56(4), 541–562 (1993)
K.C. Howell, B.T. Barden, Trajectory design and stationkeeping for multiple spacecraft in formation near the Sun-Earth L1 point, in Proceedings of the 50th International Astronautical Federation Congress, IAF/IAA Paper 99-A707 (1999)
NGO science working team, NGO assessment study report (Yellow book) ESA/SRE(2011)19
LISA International Science Team 2011, LISA assessment study report (Yellow Book) (European Space Agency) ESA/SRE(2011) 3. http://sci.esa.int/science-e/www/object/index.cfm?fobjectid=48364
D. Folta, Formation flying design and applications in weak stability boundary regions. Ann. N. Y. Acad. Sci. 1017, 95–111 (2004)
B. Buchberger, Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems. Aequationes mathematicae 4, 374–383 (1970)
M. Maggiore, Theory and experiments, Gravitational Waves, vol. 1 (Oxford University Press, Oxford, 2008)
F.B. Estabrook, H.D. Wahlquist, Response of Doppler spacecraft tracking to gravitational radiation. Gen. Relat. Gravity 6, 439 (1975)
J. Abadie et al., [LIGO and Virgo Collaborations], Sensitivity to gravitational waves from compact binary coalescences achieved during LIGO’s fifth and Virgo’s first science run, LIGO-T0900499-v19 (2010). arXiv:1003.2481
D. Shoemaker et al., Advanced LIGO anticipated sensitivity curves, LIGO-T0900288-v3 (2010). https://dcc.ligo.org/LIGO-T0900288-v3/public
M.R. Drinkwater et al., GOCE: ESA’s first earth explorer core mission. Space Sci. Rev. 108(1), 419–432 (2003)
G. Sechi et al., In-flight results from the drag-free and attitude control of GOCE satellite, in Preprints of the 18th IFAC World Congress, Milano, pp. 733–740 (2011)
S.L. Larson, W.A. Hiscock, R.W. Hellings, Sensitivity curves for spaceborne gravitational wave interferometers. Phys. Rev. D 62, 062001 (2000). arXiv:gr-qc/9909080
K. Yagi, Scientific potential of DECIGO pathfinder and testing GR with space-borne gravitational wave interferometers. Int. J. Mod. Phys. D 22, 1341013 (2013). arXiv:1302.2388
S. Barke et al., EOM sideband phase characteristics for the spaceborne gravitational wave detector LISA. Appl. Phys. B 98(1), 33–39 (2010)
M. Rakhmanov, Response of LIGO to gravitational waves at high frequencies and in the vicinity of the FSR (37.5 kHz), LIGO-T060237-00-D (2005). https://dcc.ligo.org/T060237-x0/public
R. Schnabel, N. Mavalvala, D.E. McClell, P.K. Lam, Quantum metrology for gravitational wave astronomy. Nat. Commun. 1, 121 (2010)
Nat. Phys. A gravitational wave observatory operating beyond the quantum shot-noise limit: squeezed light in application. 7, 962 (2011). arXiv:1109.2295
A. Khalaidovski, H. Vahlbruch, N. Lastzka, C. Graf, H. Luck, K. Danzmann, H. Grote, R. Schnabel, Status of the GEO 600 squeezed-light laser. J. Phys. Conf. Ser. 363, 012013 (2012). arXiv:1112.0198
B.S. Sathyaprakash, B.F. Schutz, Physics, astrophysics and cosmology with gravitational waves. Living Rev. Relat. 12, 2 (2009). arXiv:0903.0338, http://www.livingreviews.org/lrr-2009-2
A.J. Farmer, E.S. Phinney, The gravitational wave background from cosmological compact binaries. Mon. Not. R. Astron. Soc. 346, 1197 (2003). arXiv:astro-ph/0304393
V. Ferrari, S. Matarrese, R. Schneider, Mon. Not. R. Astron. Soc. 303, 247 (1999). arXiv:astro-ph/9804259
R. Brustein, M. Gasperini, M. Giovannini, G. Veneziano, Relic gravitational waves from string cosmology. Phys. Lett. B 361, 45 (1995). arXiv:hep-th/9507017
M.S. Turner, Detectability of inflation produced gravitational waves. Phys. Rev. D 55, 435 (1997). arXiv:astro-ph/9607066
K.N. Ananda, C.Clarkson, D. Wands, The cosmological gravitational wave background from primordial density perturbations. Phys. Rev. D 75, 123518 (2007). arXiv:gr-qc/0612013
C.J. Hogan, P.L. Bender, Estimating stochastic gravitational wave backgrounds with Sagnac calibration. Phys. Rev. D 64, 062002 (2001). arXiv:astro-ph/0104266
N. Seto, Correlation analysis of stochastic gravitational wave background around 0.1-1 Hz. Phys. Rev. D 73, 063001 (2006). arXiv:gr-qc/0510067
E.E. Flanagan, The Sensitivity of the laser interferometer gravitational wave observatory (LIGO) to a stochastic background, and its dependence on the detector orientations. Phys. Rev. D 48, 2389 (1993). arXiv:astro-ph/9305029
B.P. Abbott et al., LIGO Scientific and VIRGO Collaborations, An upper limit on the stochastic gravitational-wave background of cosmological origin, Nature 460, 990 (2009). arXiv:0910.5772
M. Hohmann, Propagation of gravitational waves in multimetric gravity. Phys. Rev. D 85, 084024 (2012). arXiv:1105.2555
D.M. Eardley, D.L. Lee, A.P. Lightman, Gravitational-wave observations as a tool for testing relativistic gravity. Phys. Rev. D 8, 3308 (1973)
C.M. Will, The confrontation between general relativity and experiment. Living Rev. Relat. 9, 3 (2006). arXiv:gr-qc/0510072, http://www.livingreviews.org/lrr-2009-2
J.R. Gair, M. Vallisneri, S.L. Larson, J.G. Baker, Testing general relativity with low-frequency, space-based gravitational-wave detectors. Living Rev. Relat. 16, 7 (2013). arXiv:1212.5575, http://www.livingreviews.org/lrr-2013-7
S.J. Chamberlin, X. Siemens, Stochastic backgrounds in alternative theories of gravity: overlap reduction functions for pulsar timing arrays. Phys. Rev. D 85, 082001 (2012). arXiv:1111.5661
P. Jaranowski, A. Krolak, B.F. Schutz, Data analysis of gravitational - wave signals from spinning neutron stars. 1. The signal and its detection. Phys. Rev. D 58, 063001 (1998). arXiv:gr-qc/9804014
D.I. Jones, N. Andersson, Gravitational waves from freely precessing neutron stars. Mon. Not. R. Astron. Soc. 331, 203 (2002). arXiv:gr-qc/0106094
N. Andersson, K.D. Kokkotas, N. Stergioulas, On the relevance of the r mode instability for accreting neutron stars and white dwarfs. Astrophys. J. 516, 307 (1999). arXiv:astro-ph/9806089
R.N. Manchester, G.B. Hobbs, A. Teoh, M. Hobbs, The Australia Telescope National Facility pulsar catalogue. Astron. J. 129, 1993 (2005). arXiv:astro-ph/0412641
J. Abadie et al., [LIGO Scientific and Virgo Collaborations], Beating the spin-down limit on gravitational wave emission from the Vela pulsar. Astrophys. J. 737, 93 (2011). arXiv:1104.2712
B. Abbott et al., [LIGO Scientific Collaboration], Setting upper limits on the strength of periodic gravitational waves using the first science data from the GEO 600 and LIGO detectors. Phys. Rev. D 69, 082004 (2004). arXiv:gr-qc/0308050
J. Aasi et al., [The LIGO Scientific and the Virgo Collaboration], Einstein@Home all-sky search for periodic gravitational waves in LIGO S5 data. Phys. Rev. D 87, 042001 (2013). arXiv:1207.7176
R. Prix, S. Giampanis, C. Messenger, Search method for long-duration gravitational-wave transients from neutron stars. Phys. Rev. D 84, 023007 (2011). arXiv:1104.1704
M.C. Miller, E.J.M. Colbert, Intermediate - mass black holes. Int. J. Mod. Phys. D 13, 1 (2004). arXiv:astro-ph/0308402
M. Pasquato, Croatian Black Hole School 2010 lecture notes on IMBHs in GCs, arXiv:1008.4477
P. Amaro-Seoane, M. Freitag, Intermediate-mass black holes in colliding clusters: implications for lower-frequency gravitational-wave astronomy. Astrophys. J. 653, L53 (2006). arXiv:astro-ph/0610478
P. Amaro-Seoane, M.C. Miller, M. Freitag, Gravitational waves from eccentric intermediate-mass black hole binaries. Astrophys. J. 692, L50 (2009). arXiv:0901.0604
J.M. Fregeau, S.L. Larson, M.C. Miller, R.W. O’Shaughnessy, F.A. Rasio, Observing IMBH-IMBH binary coalescences via gravitational radiation. Astrophys. J. 646, L135 (2006). arXiv:astro-ph/0605732
I. Mandel, D.A. Brown, J.R. Gair, M.C. Miller, Rates and characteristics of intermediate-mass-ratio inspirals detectable by advanced LIGO. Astrophys. J. 681, 1431 (2008). arXiv:0705.0285
K. Yagi, Gravitational wave observations of galactic intermediate-mass black hole binaries with DECIGO path finder. Class. Quantum Gravity 29, 075005 (2012). arXiv:1202.3512
J. Abadie et al., [LIGO Scientific and Virgo Collaborations], Search for gravitational waves from intermediate mass binary black holes. Phys. Rev. D 85, 102004 (2012). arXiv:1201.5999
J. Abadie et al., [LIGO Scientific and Virgo Collaborations], All-sky search for gravitational-wave bursts in the second joint LIGO-Virgo run. Phys. Rev. D 85, 122007 (2012). arXiv:1202.2788
K. Somiya, K. Goda, Y. Chen, E.E. Mikhailov, Isolation of gravitational waves from displacement noise and utility of a time-delay device. J. Phys. Conf. Ser. 66, 012053 (2007) arXiv:gr-qc/0610117
K. Somiya, Y. Chen, K. Goda, E.E. Mikhailov, Utility investigation of artificial time delay in displacement-noise-free interferometers. Phys. Rev. D 76, 022002 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Wang, Y. (2016). Octahedron Configuration for a Displacement Noise-Canceling Gravitational Wave Detector in Space. In: First-stage LISA Data Processing and Gravitational Wave Data Analysis. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-26389-2_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-26389-2_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-26388-5
Online ISBN: 978-3-319-26389-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)