Gravitational Wave Background from Astrophysical Sources

1. The 6th Korea-Japan Workshop On KAGRA:June 20-21 at NAOJ, Tokyo, JAPAN Gravitational Wave Background fromAstrophysical Sources Zhu, Zong-Hong 朱, 宗 宏 (zhuzh@bnu.edu.cn) Beijing Normal University, Beijing 100875, China 北京 師範 大学, 北京 100875, 中国 【A summary of recent work in my group】

2. GW Background fromAstrophysical Sources • Stochastic Gravitational Wave Background from Neutron Star r-mode Instability Revisited X.-J. Zhu, X.-L. Fan, Z-HZ2011ApJ 729, 59 • Stochastic Gravitational Wave Background from Coalescing Binary Black Holes X.-J. Zhu, ………, Z-HZ2011ApJ 739, 86 • On the Gravitational Wave Background from Compact Binary Coalescences in the Band of Ground-based Interferometers X.-J. Zhu, ………, Z-HZ2013MNRAS 431, 882 Korea-Japan Workshop on KAGRA

3. Korea-Japan Workshop on KAGRA

4. Background Radiations from Big Bang Korea-Japan Workshop on KAGRA

5. Characterization of CGWB:gw The energy density parametergwisis defined as the GW energy densityper logarithmic frequency interval at observed frequency f , dividedby the critical energy densityrequired to close the Universe today. Korea-Japan Workshop on KAGRA

6. Characterization of CGWB: Sh (f) If ma , mb are two unit vectors orthogonal to  and to each other, the polarization tensors can be written as A Stochastic Background (isotropic, unpolarized and stationary)  Sh(f) is the spectral density which has dimensions Hz –1and satisfy Sh(f)=Sh(-f) and relates to gw(f) as Korea-Japan Workshop on KAGRA

7. Characterization of CGWB: nf For particle physicists, gravitational wave is nothing but gravitons. So one can also characterize gravitational wave using the number density of gravitons in the phase space, n(x,k). For a CGWB, it depends only on f  The large number 1037 just means that a detectable CGWB is therefore exceedingly classical, nk >>1. Korea-Japan Workshop on KAGRA

8. Primordial Gravitational Wave Background From the LIGO & Virgo Collaboration, 2009, Nature Korea-Japan Workshop on KAGRA

9. Two origins of SGWB Primordial GWs CMB Astrophysical sources LISA Korea-Japan Workshop on KAGRA

10. Why astrophysical background ? Korea-Japan Workshop on KAGRA Primordial GWs from the big bang - the holy grail (rich information about the early universe) Astrophysical background (AB) - mask the primordial background - star formation history, source population The strength of the AB depends on source ratesand individual energy emissions - high rate & strong energy emission  strong background

11. Basics of AGWB For GWB of astrophysical origin, ΩGW depends on the average GW energy released by individual sources and the rate at which these events happen throughout the Universe E.g., for CBC events, the average chirp mass and the coalescence rate (the local rate and its cosmic evolution) A lot of uncertainties should be considered properly, … , in order to tell what is the chance to detect it and what can we learn from detection or non-detection(the motivation) Korea-Japan Workshop on KAGRA

12. Behaviours in time • Duty cycle (DC): the ratio between the average event durationand the time interval between successive events. DC=0.1, Shot noise arXiv: 1101.2762 DC=1, Popcorn noise DC=100, Gaussian background Korea-Japan Workshop on KAGRA

13. A stochastic GW background from CBC • Millions of binary mergers happening around the Universe every year. Blue: GWB+white noise Red: GWB only Korea-Japan Workshop on KAGRA

14. Spectrogram GWB only GWB+white noise Korea-Japan Workshop on KAGRA

15. A simple power law model Based on the practical theorem in Phinney (2001) Rate evolution E(z) assuming the CSFR in Hopkins & Beacom (2006) Korea-Japan Workshop on KAGRA

16. Rate evolution based on CSFRs Korea-Japan Workshop on KAGRA

17. Effects of CSFR and delay time - Linear Calculated for 10 models of e(z): 5 CSFRs and Two tmin = 10 or 100 Myr Korea-Japan Workshop on KAGRA

18. Complete waveforms BBH Fig. from Zhu et al. 2011 BNS BNS– A Gaussian spectrum is used to approximate the Post-merger emission recently calculated in Bauswein et al.(2012); see Table 2 & Figs.7&8 therein BBH– phenomenological inspiral-merger-ringdown waveforms in Ajith et al. (2011) BH-NS– assuming the same as BBH, see Shibata & Taniguchi (2011) Korea-Japan Workshop on KAGRA

19. Improved models (1) Korea-Japan Workshop on KAGRA Compared to previous estimates and our simple model

20. Improved models (2) Gaussian NS/BH mass Four models of BH mass Korea-Japan Workshop on KAGRA Complete waveforms + NS/BH mass distributions

21. Is a simple power law model good enough? YES Using overlap reduction functions for the 10 pairs among 5 advanced IFOs (H, L, V, K, A) A: AIGO, assumed in Perth, Australia, having the same sensitivity as aLIGO * Signal power ~ f-7/3 * Improvement on low-f sensitivity is very impor-tant for detection Relative variations in the estimated mean of CC signals less than ~ 4% if a simple power law rather than the accurate model used Korea-Japan Workshop on KAGRA

22. Implications ☺Effects of CSFRs and delay times are linear below ~100 Hz and can be represented with a single parameter ☺ΩGW (below 100 Hz) well described by 3 parameters: ☺ Such a simple power law model is sufficient to be used as a search template, and is also useful/handy for parameter estimation, i.e., the coalescence rate and average chirp mass (regardless of chirp mass distribution) Korea-Japan Workshop on KAGRA

23. Detectability advanced network: combining 10 pairs of 5 advanced IFOs S/N = 3, one year observation at design sensitivities The γ( f ) = 1 curve is consistent with Wu et al. 2012 Note: BH-NS r0 is set to be 0.03 Korea-Japan Workshop on KAGRA

24. Overlap reduction function the distance between two detectors Above this frequency, γ (f ) decays rapidly towards zero. Korea-Japan Workshop on KAGRA

25. https://dcc.ligo.org/LIGO-T0900288/public

26. Prospects for advanced detectors • Given the current realistic rate predictions and observational NS/BH mass measurements, we have S/N (1 year observation): • 1 for aLIGO standard sensitivity 4 years S/N =2 • 1.3 for a network of detectors  3 years • 1.5 for aLIGO tuning with the best low-f sensitivity  2 years, • Better than 5 detectors! 1 year, S/N=3, aHL Korea-Japan Workshop on KAGRA

27. A bit more on the resolvability • Individual sources constituting an AGWB are distributed at different distances • The closest/loudest ones can be individually identified and subtracted away • In this way, the BNS background could be almost entirely removed for the proposed Big Bang Observer • We show that for ET there is a significant (residual) foreground signal dominated by sub-threshold BNS signals • Will such a foreground be resolvable ? Korea-Japan Workshop on KAGRA

28. Resolve a CBC background ? a:the BNS background without any noise; Resolvable as one can actually ‘see’ a 50 times higher rate and overall amplitude reduced by 50 b:the BNS background plus some (arbitrarily) modest amount of Gaussian white noise b Note: the background signals stand out at below ~ 20 Hz simply because the added noise is too weak Korea-Japan Workshop on KAGRA

29. Subtraction of detectable signals The strongest signals are to be “subtracted” Korea-Japan Workshop on KAGRA

30. How the subtraction helps 1/2 1/10 1/200 Residual foreground noise (in spectral density) Reduction in ΩGW(f ) Korea-Japan Workshop on KAGRA

31. Unique properties of the CBC background • In fact, it is just a collection of discrete transient events randomly coming from the sky (in ground-based frequency band) • Their waveforms are well predicted • Currently there is no search algorithm designed or optimised to such a population • New method could improve over standard cross correlation statistic (i.e., isotropic and stochastic) by employing full information Korea-Japan Workshop on KAGRA

32. Outlook of SB searches with aLIGO CBC is the best understood source of GWs for ground-based detectors We are likely to detect a GWB from CBCs – low frequency sensitivity is essential (Non-)detection of a GWB will (constrain) estimate the coalescence rate and average chirp mass A CBC foreground must be considered in searches for other SGWBs (As it is well defined, it should not be a big issue for primordial GWB searches?) Full information about the population should be exploited to enhance the detectability Korea-Japan Workshop on KAGRA

33. Landscape of primordial GWBs CBC Figure from Nature 460, 990 (2009) Korea-Japan Workshop on KAGRA

34. Summary aLIGO SB searches: mainly to constrain various models However, CBC provides the most promising target, likely to be detected Multiple sources (of SB) should be considered simultaneously in the future searches The CBC background is well modelled, and thus could not be a big issue for primordial GWBs (?) Korea-Japan Workshop on KAGRA

38. Thanks for your attention !