Skip to main content
SpringerLink
Log in
Book cover

First-stage LISA Data Processing and Gravitational Wave Data Analysis pp 139–174Cite as

Octahedron Configuration for a Displacement Noise-Canceling Gravitational Wave Detector in Space

  • Chapter
  • First Online:

  • 860 Accesses

Part of the book series: Springer Theses ((Springer Theses))

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.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. G.M. Harry, LIGO Scientific Collaboration, Advanced LIGO: the next generation of gravitational wave detectors. Class. Quantum Gravity 27, 084006 (2010)

    Google Scholar 

  2. The Virgo Collaboration, Advanced Virgo baseline design, VIRC027AC09 (2009). https://tds.ego-gw.it/itf/tds/file.php?callFile=VIR-0027A-09.pdf

  3. 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

  4. 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

  5. B. Owen, Probing neutron stars with gravitational waves, LIGO-T0900053 (2009). arXiv:0903.2603

  6. B. Allen, J.D. Romano, Detecting a stochastic background of gravitational radiation: sensitivities. Phys. Rev. D 59, 102001 (1999). arXiv:gr-qc/9710117

  7. M. Maggiore, Gravitational wave experiments and early universe cosmology. Phys. Rep. 331, 283 (2000). arXiv:gr-qc/9909001

    Google Scholar 

  8. 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)

    Google Scholar 

  9. P. Amaro-Seoane et al., eLISA: astrophysics and cosmology in the millihertz regime. GW Notes 6, 4–110 (2013). arXiv:1201.3621

  10. M. Ando et al., DECIGO and DECIGO pathfinder. Class. Quantum Gravity 27, 084010 (2010)

    Article  ADS  Google Scholar 

  11. Y. Chen et al., Interferometers for displacement-noise-free gravitational-wave detection. Phys. Rev. Lett. 97, 151103 (2006). arXiv:gr-qc/0603054

  12. S. Kawamura, Y. Chen, Displacement-noise-free gravitational-wave detection. Phys. Rev. Lett. 93, 211103 (2004). arXiv:gr-qc/0405093

  13. Y. Chen, S. Kawamura, Displacement- and timing-noise free gravitational-wave detection. Phys. Rev. Lett. 96, 231102 (2006). arXiv:gr-qc/0504108

  14. 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

  15. M. Otto, G. Heinzel, K. Danzmann, TDI and clock noise removal for the split interferometry configuration of LISA. Class. Quantum Gravity 29, 205003 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  16. 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)

    Article  ADS  MATH  Google Scholar 

  17. 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)

    Google Scholar 

  18. NGO science working team, NGO assessment study report (Yellow book) ESA/SRE(2011)19

    Google Scholar 

  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

  20. D. Folta, Formation flying design and applications in weak stability boundary regions. Ann. N. Y. Acad. Sci. 1017, 95–111 (2004)

    Article  ADS  Google Scholar 

  21. B. Buchberger, Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems. Aequationes mathematicae 4, 374–383 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  22. M. Maggiore, Theory and experiments, Gravitational Waves, vol. 1 (Oxford University Press, Oxford, 2008)

    Google Scholar 

  23. F.B. Estabrook, H.D. Wahlquist, Response of Doppler spacecraft tracking to gravitational radiation. Gen. Relat. Gravity 6, 439 (1975)

    Article  ADS  Google Scholar 

  24. 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

  25. D. Shoemaker et al., Advanced LIGO anticipated sensitivity curves, LIGO-T0900288-v3 (2010). https://dcc.ligo.org/LIGO-T0900288-v3/public

  26. M.R. Drinkwater et al., GOCE: ESA’s first earth explorer core mission. Space Sci. Rev. 108(1), 419–432 (2003)

    Article  ADS  Google Scholar 

  27. 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)

    Google Scholar 

  28. 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

  29. 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

    Google Scholar 

  30. S. Barke et al., EOM sideband phase characteristics for the spaceborne gravitational wave detector LISA. Appl. Phys. B 98(1), 33–39 (2010)

    Article  ADS  Google Scholar 

  31. 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

  32. R. Schnabel, N. Mavalvala, D.E. McClell, P.K. Lam, Quantum metrology for gravitational wave astronomy. Nat. Commun. 1, 121 (2010)

    Google Scholar 

  33. Nat. Phys. A gravitational wave observatory operating beyond the quantum shot-noise limit: squeezed light in application. 7, 962 (2011). arXiv:1109.2295

  34. 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

    Google Scholar 

  35. 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

  36. 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

    Google Scholar 

  37. V. Ferrari, S. Matarrese, R. Schneider, Mon. Not. R. Astron. Soc. 303, 247 (1999). arXiv:astro-ph/9804259

  38. R. Brustein, M. Gasperini, M. Giovannini, G. Veneziano, Relic gravitational waves from string cosmology. Phys. Lett. B 361, 45 (1995). arXiv:hep-th/9507017

    Google Scholar 

  39. M.S. Turner, Detectability of inflation produced gravitational waves. Phys. Rev. D 55, 435 (1997). arXiv:astro-ph/9607066

    Google Scholar 

  40. 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

  41. C.J. Hogan, P.L. Bender, Estimating stochastic gravitational wave backgrounds with Sagnac calibration. Phys. Rev. D 64, 062002 (2001). arXiv:astro-ph/0104266

  42. N. Seto, Correlation analysis of stochastic gravitational wave background around 0.1-1 Hz. Phys. Rev. D 73, 063001 (2006). arXiv:gr-qc/0510067

  43. 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

    Google Scholar 

  44. 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

  45. M. Hohmann, Propagation of gravitational waves in multimetric gravity. Phys. Rev. D 85, 084024 (2012). arXiv:1105.2555

  46. 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)

    Article  ADS  Google Scholar 

  47. 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

  48. 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

  49. 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

  50. 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

  51. D.I. Jones, N. Andersson, Gravitational waves from freely precessing neutron stars. Mon. Not. R. Astron. Soc. 331, 203 (2002). arXiv:gr-qc/0106094

    Google Scholar 

  52. 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

    Google Scholar 

  53. 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

    Google Scholar 

  54. 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

  55. 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

  56. 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

  57. 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

    Article  ADS  Google Scholar 

  58. M.C. Miller, E.J.M. Colbert, Intermediate - mass black holes. Int. J. Mod. Phys. D 13, 1 (2004). arXiv:astro-ph/0308402

    Google Scholar 

  59. M. Pasquato, Croatian Black Hole School 2010 lecture notes on IMBHs in GCs, arXiv:1008.4477

  60. 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

    Google Scholar 

  61. 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

    Google Scholar 

  62. 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

    Google Scholar 

  63. 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

    Google Scholar 

  64. 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

    Google Scholar 

  65. 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

  66. 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

  67. 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

    Google Scholar 

  68. 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)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Physics, The University of Western Australia, Perth, Australia

    Yan Wang

Authors
  1. Yan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yan Wang .

Rights and permissions

Reprints 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

Publish with us

Policies and ethics

Search

Navigation