Axion Bosenova and. Gravitational Waves

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1 Axion and Gravitational Waves Hirotaka Yoshino Hideo Kodama "KEK# PTP128, 153 (2012) PTEP2014, 043E02 (2014) arxiv:1406.xxxx (in progress) 3!day workshop "holographic YITP at Kyoto U. "May 26th, 2014#

2 CONTENTS Introduction PTP128, 153 (2012) PTEP2014, 043E02 (2014) Constraining string axion models from GW observations in Progress Summary

3 Introduction

4 Very interesting era of GR Advanced LIGO Advanced VIRGO KAGRA One of the interesting possibilities is to find new physics beyond GR!

5 Can we find a signal of string theory? Arvanitaki, Dimopoulos, Dubvosky, Kaloper, March!Russel, PRD81 "2010#, Maybe Yes, if there are String Axions with very tiny mass In string theory, many moduli appear when the extra dimensions get compactified. Some of them "10!100# are expected to behave like scalar fields with very tiny mass, which are called string axions. CMB Polarization Matter Power Spectrum Anthropically Constrained Black Hole Super-radiance Decays Inflated Away ! ! ! Axion Mass in ev 3! QCD axion AXIVERSE SCENARIO

6 Axion field around a rotating BH Axion field extracts BH rotational energy and forms an axion cloud Gravitational atom Detweiler, PRD22 "1980#, Zouros and Eardley, Ann. Phys. 118 "1979#, 139.

7 Kerr BH Metric ( a ds 2 2 sin 2 ) θ = dt 2 2a sin2 θ(r 2 + a 2 ) dtdφ Σ Σ [ (r 2 + a 2 ) 2 a 2 sin 2 ] θ + sin 2 θdφ 2 + Σ Σ dr2 + Σdθ 2 Σ = r 2 + a 2 cos 2 θ, = r 2 + a 2 2Mr. J = Ma Ergoregion ξ µ becomes spacelike Energy density can be T µν ξ µ n ν < 0 BH condition: ω <mω H

8 Gravitational Atom Massive Klein!Gordon field 2 Φ µ 2 Φ =0 Φ = Re[e iωt R(r)S(θ)e imφ ] R = u r2 + a 2 d 2 u dr 2 + [ ω 2 V (ω) ] u =0 ω = ω R + i ω I Unstable if positive I II III IV condition ω < Ω H m! r * /M V

9 Growth rate Growth rate "continued fraction method# Dolan, PRD76 "2007#, e-06 1e-07 l = 1, m = 1 l = 2, m = 2 a = a = 0.99 a = 0.95 a = 0.9 a = 0.8 a = 0.7 Im(! /!) 1e-08 1e-09 l = 3, m = 3 1e-10 Typical time scale: 1e M! M = M ω I M min. ω I M day

10 Scalar field amplitude Gross phenomena of the BH!axion system T sr 10 7 M Time

11 Gross phenomena of the axion!bh system Scalar field amplitude ϕ 1 T sr 10 7 M Time Yoshino and Kodama, PTP128, 153 "2012#

12 Gross phenomena of the axion!bh system Scalar field amplitude ϕ 1 T sr 10 7 M V = f 2 aµ 2 [1 cos(φ/f a )] 2 ϕ µ 2 sin ϕ =0 ϕ Φ f a Time Yoshino and Kodama, PTP128, 153 "2012#

13 Gross phenomena of the axion!bh system Scalar field amplitude ϕ 1 Φ T sr 10 7 M r Time Yoshino and Kodama, PTP128, 153 "2012#

14 Gross phenomena of the axion!bh system Scalar field amplitude T BN 100M ϕ 1 T sr 10 7 M Time

15 Gross phenomena of the axion!bh system Scalar field amplitude T BN 100M ϕ 1 T sr 10 7 M Time

16 Gross phenomena of the axion!bh system Scalar field amplitude T BN 100M ϕ 1 GW GW GW T sr 10 7 M If the bosenova happens at Cygnus X!1 ω GW 10 2 Hz GW amplitude is marginal to be detected by 2nd generation ground based detectors "order estimate# Time Yoshino and Kodama, PTP128, 153 "2012#

17 Gross phenomena of the axion!bh system Scalar field amplitude T BN 100M ϕ 1 GW GW GW T sr 10 7 M BH!axion system also emits continuous GWs ω GW 2µ Yoshino and Kodama, PTEP2014, 043E02 (2014) Gravitational Lihgthouse by Vitor s expression Time

18 Gross phenomena of the axion!bh system Scalar field amplitude T BN 100M ϕ 1 GW GW GW T sr 10 7 M BH!axion system also emits continuous GWs ω GW 2µ ( ) 2 Ea = C nl (Mµ) 4l+10 de a dt M dt de GW Yoshino and Kodama, PTEP2014, 043E02 (2014) Gravitational Lihgthouse by Vitor s expression Time

19 Gross phenomena of the axion!bh system Scalar field amplitude T BN 100M ϕ 1 GW GW GW T sr 10 7 M Today, I discuss how to constrain the string axion models from observations of continuous GWs Gravitational Lihgthouse by Vitor s expression Time

20 Constraining string axion models from GW observation

21 LIGO s science runs "1# PRD69, "2004#; ; arxiv: $gr!qc% They looked for continuous waves from distorted pulsars Detectable amplitude can be made smaller by increasing observation time h rss h T obs

22 LIGO s continuous wave search No GWs have been detected, upper limit on the amplitude is given.

23 Our idea "1# Consider continuous waves from BH!axion system 50 Hz f 1200 Hz ev µ ev If we assume M 15M, Mµ 0.3 We consider axion cloud in the l = m = 1 mode We use the approximate formula for small Mµ The wave form is same as the distorted pulsar case ( Ea ) ) Amplitude: h 0 M (µm) 6 ( M d

24 Our idea "2# We adopt the axion cloud energy when the nonlinear self! interaction becomes important Φ max f a 1 Ea 8πe 2 M ( fa M p ) 1 (µm) ( f a GeV ) 2 ( M 15M ) 3 ( µ ev ) ( ) 2 1 d <h UL 1kpc In order to exclude the situation where gravitational backreaction is significant, we require E a M < 0.05 f a GeV < 0.1 ( M 15M ) 2 ( µ ) ev

25 Let us consider Cygnus X!1 Cygnus X"1 M 15M! 17 a > 0.9 Log10! fa #GeV$" d 1.86 kpc!?" 16 Excluded LIGO 15 aligo 14 Allowed 13 0 McClintock, et al., arxiv: !3690&astro!ph' 5.! 10"13 Μ #ev$ 1.! 10"12 1.5! 10"12 2.! 10"12

26 Remark The result of the continuous wave search cannot be used in our case because In the data analysis, isolated pulsar is assumed. Cygnus X!1 is a binary system, and therefore, GW frequency fluctuates by the Doppler shift The data analysis strongly depend on the assumed situation If the target search of continuous waves from the Cygnus X!1 is carried out, that kind of constraint can be obtained.

27 Dependence on the distance M BH 15M Some estimates give the BH number in our galaxy as Timms, Woosley, Weaver, ApJ457, 834 "1996# ? Excluded The averaged distance in the neighbouring BHs is expected to be 7 15 pc Log 10 fa GeV d 1500 pc 150 pc 15 pc Allowed There might exist invisible isolated BH at relatively close position Μ ev

28 Summary

29 Summary It is possible to constrain string axion models from existing LIGO observational data. Target search from continuous GWs from Cygnus X!1 is required to obtain rigorous constraint. Invisible isolated solar mass BHs are likely to exist relatively close to us, and this suggests that string axions may be constrained more strongly.