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Localization of GW sources and implication for cosmology

This article discusses the localization capabilities of next-generation gravitational wave detectors, such as the Einstein Telescope (ET) and Cosmic Explorer (CE), and their implications for cosmology. It also explores the concept of using GW sources as "standard sirens" for measuring cosmological parameters, including the Hubble constant.

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Localization of GW sources and implication for cosmology

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  1. Localization of GW sources and implication for cosmology Wen Zhao Department of Astronomy, University of Science and Technology of China Based on: WZ, C.van Broeck, D.Baskaran & T.G.F.Li, Phys.Rev.D, 2011 WZ & L.Q.Wen, arXiv: 1710.05325 WZ & L.Santos, arXiv:1710.10055

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  3. CMBdetection on GW in the lowest frequency range

  4. PTA detection on GW in the middle frequency range

  5. LIGO detection on GW in the high frequency range

  6. GW detectors

  7. Third-generation (3G) gravitational-wave detectors • Two leading proposals are under consideration: Einstein Telescope (ET) in Europe and Cosmic Explorer (CE) in the US. • ET consists of three Michelson interferometers with 10 km long arms, arranged to form an equilateral triangle. Two different sensitivity estimates have been put forward for the ET, named ET-B and ET-D. The low frequency cutoff is 1Hz, in comparison with 10 Hz for aLIGO. • CE will keep L-shaped configuration, but the length of arms will be increased to 40 km. The low frequency cutoff is 5Hz.

  8. For 3G detector networks: Sources localization • In general, the localization capabilities of a single 2G GW detector are rather poor. GW detector network with large baselines is therefore needed to facilitate better source localization. • However, for 3G detectors, the low frequency cutoff will be extended to several Hz. The BNS singles can be in the band for several hours, or even for several days. • Due to the rotation of the Earth, an individual detector can be effectively treated as a network (similar to LISA) including a set of detectors at different sites along the detector’s trajectory of the Earth, which observe a given GW event at different time. • From the noise curves of ET and CE, we expect their localization capabilities as follows: ideal > ET-D > ET-B >CE.

  9. Localization capabilities of one detector

  10. Dependence of source localization on the low-frequency cutoff • For binary coalescence, the duration of the signal in a detector band is a strong function of the detector’s low-frequency cutoff:

  11. Localization capabilities of 2-detector network

  12. Localization capabilities of 3-detector network

  13. GW Sources as ‘Standard Sirens’ • In 1986, Schutz found that the luminosity distance of the binary neutron stars (or black hole) can be independently determined by observing the G.W. generated by this system. If we can also find the EM counterpart, the redshiftcan also be determined.Thus the dL-z relation can be used to study the evolution of universe. This is the so-called: standard sirens.(Schutz,Nature,1986) characters：1. non-EM method to study the cosmology 2. independent of “cosmic distance ladder” * Measurement of Hubble Constant [Ground-based] Adv.LIGO，Adv.VIRGO (BNS, NSBH) * Detection of Dark energy [Ground-based] Einstein Telescope (BNS, NSBH) [Space-based] LISA (SMBBH) [Space-based] BBO (BNS, NSBH)

  14. GW Sources as ‘Standard Sirens’ • In 1986, Schutz found that the luminosity distance of the binary neutron stars (or black hole) can be independently determined by observing the G.W. generated by this system. If we can also find the EM counterpart, the redshiftcan also be determined.Thus the dL-z relation can be used to study the evolution of universe. This is the so-called: standard sirens.(Schutz,Nature,1986) characters：1. non-EM method to study the cosmology 2. independent of “cosmic distance ladder” * Measurement of Hubble Constant [Ground-based] Adv.LIGO，Adv.VIRGO (BNS, NSBH) * Detection of Dark energy [Ground-based] Einstein Telescope (BNS, NSBH) √ [Space-based] LISA (SMBBH) [Space-based] BBO (BNS, NSBH)

  15. GW Sources as ‘Standard Sirens’

  16. GW Sources as ‘Standard Sirens’ • How to determine the ‘redshift’？ * Searching for the host galaxy by GW detectors with very high position resolution（Space-based detectors or nearby sources by detector network） （Throne, 1987; Wen & Chen, PRD, 2010） * Detecting additional contributions of GW phases caused Tidal effects (5PN for system with at least one NS ) （Messenger & Read, PRL, 2012） * Assuming a narrow mass distribution of NS (for BNS and NSBH ) （Taylor, Gair and Mandel, PRD, 2012） * Searching for EM counterparts: GRBs, X-ray bursts, etc.

  17. What are the EM counterparts? • Short-hard Gamma-ray bursts • Kilo-novae and radio afterglow • Alternative NS-NS merger product: A hyper-massive, millisecond, highly magnetized NS (magnetar)

  18. Measurement of Hubble constant • GW170817: z=0.0103, dL=(43.8+2.9-6.9)Mpc. According to Hubble law, the value of H0 can be derived as follows. (LVC collaboration 2017) • Using GW170817 to calibrate the cosmic distance ladder (SNIa), we find the calibration results are consistent with the tradition Cepheid calibration. And the calibration accuracies of both methods are comparable. • In 3G era, if 10 BNSs or NSBHs at z=0.1 with known redshifts are detected by 2ETD network, the Hubble constant H0 can be measured with an accuracy of 0.9%. It will reduced to 0.6% for 3CE or 3ETD networks.

  19. Expanding Universe and Dark Energy • Let us work with the FLRW universes, which are described by k=0,1,-1 describes the flat, closed and open universe, respectively. • We consider the universe is filled by the cold dust (baryon and dark matter) and dark energy with the equation of state (EoS)

  20. Short-hard Gamma-ray burst and Gravitational waves

  21. Short-hard Gamma-ray Bursts • We assume gamma radiation is emitted in a narrow cone at a rangeiota ≤ 20o. • We only consider the low redshift sources with z ≤ 2. • Total uncertainty of the luminosity distance is estimated by

  22. Gravitational Wave Standard Sirens

  23. As a conservative estimation, we assume 1000 sources [the number of total GW sources is ~ (several x105)/year)] will be observed by both EM and GW ways. • In addition to the number of the sources, the redshift distribution of the sources might also play a crucial role for the detection of dark energy. * uniform distribution [ r(z) = constant ] * non-uniform distribution [ r(z) peaks at z = 1 ] (Schneider et al 2001)

  24. How to break the parameter degeneracy?--- Planck CMB Prior • Observations of CMB are always used as the required prior for the detection of dark energy. • CMB is very sensitive for the determination of ‘curvature’,‘baryon’ and ‘dark matter’, which is just complementary with GW method. • The Fisher matrix for CMB is • Now, let us combine Planck (CMB) and ET (GW) method.

  25. ET (GW) & JDEM (BAO) & SNAP (SNIa)

  26. Detection abilities of 3G networks • We apply the similar analysis to the 3G detector networks. • Assuming the GW sources with known redshift, and the total number is N, we calculate the distance uncertainties using 5-parameter Fisher matrix. • In the LCDM model, we constrain only the dark energy parameters with GW standard sirens, which are quantified by:

  27. Detection abilities of 3G networks

  28. Thanks!

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