A brief history of gravitational-wave research and the gravitational-wave spectrum

A brief history of gravitational-wave research and the gravitational-wave spectrum

Wei-Tou Ni

National Tsing Hua University

Refs: (i) WTN, GW classification, space GW detection sensitivities and AMIGO arXiv:1709.05659 [gr-qc] July 4, 2017 Plenary talk at ICGAC-IK15

(ii) S. Kuroyanagi, L-W Luo and WTN, GW sensitivities over all frequency band (iii) K Kuroda, WTN and W-P Pan, GWs: Classification, methods of detection,

sensitivities, and sources, IJMPD 24 (2015) 1530031

(iv) C-M Chen, J Nester and WTN, A brief history of GW research, Chin. J. P. (2017) (v) WTN, GW detection in space IJMPD 25 (2016) 1530002

Outline

• Earth History

• Interferometric Detection of GW

• Discovery, Black hole distribution and Multi-Messenger Astronomy

• GW spectrum and detection sensitivities

• Cosmic Band, Quaser Astrometry Band and PTA band

• Space GW detection, new LISA and Super-ASTROD and AMIGO, Middle-

Observation-Tech Gap 100 years ago

• 1916, 1918 Einstein predicted GW and derived the quadrupole radiation formula

• White dwarf discovered in 1910 with its density soon estimated; GWs from white dwarf binaries in our Galaxy form a stochastic GW background

(confusion limit for space GW detection: strain, 10^(-20) in 0.1-1mHz band).

[Periods: 5.4 minutes (HM Cancri) to hours](3 mHz)

• One hundred year ago, the sensitivity of astrometric observation through the atmosphere around this band is about 1 arcsec. This means the strain

sensitivity to GW detection is about 10

; 15 orders away from the required sensitivity .

• Observation-Tech Gap 100 years ago: 15 orders away

Gravitational Waves – Ripples in Spacetime

• Monochromatic

A single frequency plane GW

• Wave form in time t,

Spectral form in frequency f

• Noise power amplitude

<n²(t)> = ∫₀^∞(df) S_n(f), h_n(f)  [f S_n(f)]^1/2

• Characteristic amplitude

GW propagation direction: z GR

GR

In harmonic gauge plane GW h_μν(n x + n y + n z−ct) = h_μν(U)

Gap largely bridged

• First artificial satellite Sputnik launched in 1957.

• First GW space mission proposed in public in 1981 by Faller & Bender

• LISA proposed as a joint ESA-NASA mission;

LISA Pathfinder success- fully performed.

• The drag-free tech is fully demonstrated paving the road for GW space missions.

92 days 1440 orbits 83.60 kg mass

空间引力波探测

A Compilation of GW Mission Proposals LISA Pathfinder

Launched on December 3, 2015

太极

The observation and technology gap 100 years ago in the 10 Hz – 1 kHz band

• In the LIGO discovery of 2 GW events and 1 probable GW candidate, the maximum peak strain intensity is 10

; the frequency range is 30-450 Hz.

• Strain gauge in this frequency region could reach 10

with a fast recorder about 100 years ago;

• thus, the technology gap would be 16 orders of magnitudes.

• Michelson interferometer for Michelson-Morley experiment

has a strain (Δl/l) sensitivity of 5  10

with 0.01 fringe detectability and 11 m path length;

• however, the appropriate test mass suspension system with fast (30-450 Hz

in the high-frequency GW band) white-light observing system is lacking.

Weber Bar (50 Years ago) 10 orders of gap abridged

• OBSERVATION OF THE THERMAL FLUCTUATIONNS OF A GRAVITATIONAL-WAVE DETECTOR* J. Weber

PRL 1966 (Received 3 October 1966)

Strains as small as a few parts in 10¹⁶ are observable for a compressional mode of a large cylinder.

• GRAVITATIONAL RADIATION* J. Weber PRL 1967 (Received 8 February 1967)

• The results of two years of operation of a 1660-cps

gravitational-wave detector are reviewed. The possibility that some gravitational signals may have been observed cannot completely be ruled out. New gravimeter-noise

Sinsky’s

Calibration

in Weber’s

Lab

The start of precision laser interferometry for GW detection

(left) Interferometer system noise measurement at 5 kHz of Moss, Miller and Forward (1971); (right) Schematic of Malibu Laser Interferometer GW

Antenna of Forward (1978)

The fundamental noise sources of Weiss 1972

• km-sized interferometer proposed

• a. Amplitude noise in the laser output power;

• b. Laser phase noise or frequency instability;

• c. Mechanical thermal noise in the antenna;

• d. Radiation-pressure noise from laser light;

• e. Seismic noise;

• f. Thermal-gradient noise;

• g. Cosmic-ray noise;

• h. Gravitational-gradient noise;

• i. Electric field and magnetic field noise.

探测引力波的原型光学干涉仪盛行时期

Flourish of Prototype Optical Interferometers for GW Detection

• Hughes Research Lab (HRL) 0.75 m TAMA 300 m

• MIT prototype interferometer 1.5 m GEO 600 m

• Glasgow prototype interferometer 10 m

• Garching prototype interferometer 30 m

• Tokyo prototype interferometer 3 m

• Paris prototype interferometer 7 m

• ISAS prototype interferometer 10 m

Laser interferometers with independently suspended mirrors. In third column, in the parenthesis either the number N of paths is

given or Fabry-Perot Finesse F is given.

重力波雷射干涉探测器 基本原理

重力波

光学共振腔 测试质量

测试质量 测试质量

光学共振腔

Interferometry for GW detection: e.g. KAGRA

Ground-based GW detectors LIGO LIGO

VIRGO KAGRA

CLIO100 ET

Weiss, Thorne, Drever, Giazotto and Barish

 1970年代，Weiss 在 MIT 建立 1.5 m 的干涉仪实验研究其噪声和灵敏度，并设法劝

说 Caltech 的Thorne 推动公里级探测引力波的雷射干涉仪。

 Thorne 也认为实验探测引力波重要，说动了物理系推动引力波实验，向世界公开征求

一位实验主持人，选中了在 Glasgow 大学建造 1 m Fabry-Perot 干涉仪原型的 Drever (1931.10.26 – 2017.3.7.) 到 Caltech 主持建造 40 m 的 Fabry-Perot 干涉仪原型。

 1980年代，MIT, Caltech 前后向 NSF 申请提出了 km 级臂长探测引力波的雷射干涉仪 计划。

 因大计划主持产生问题，待问题解决后，选中新主持人 Barish，始成功的获得了批准

，动工建造。

 Adalberto Giazotto (1940.2.1.-2017.11.16) led the development of Virgo,

emphasized the lower frequency sensitivity and led the construction of the Super Attenuator.

2016年2月11日宣布首探 Announcement of first detection

•GW151226 detected by the LIGO on December 26, 2015 at 03:38:53

•identified within 70 s by an online matched-filter search targetingUTC.

binary coalescences.

•GW151226 with S/N ratio of 13 and significance > 5σ.

•The signal ~ 1 s, about 55 cycles from 35 to 450 Hz, reached 3.4 (+0.7,−0.9) × 10^(−22). source-frame initial BH masses: 14.2 (+8.3,−3.7)M_⊙ and 7.5 (+2.3,−2.3)M_⊙, the final BH mass is 20.8 (+6.1,−1.7)M_⊙.

•1 BH has spin greater than 0.2. luminosity distance 440 (+180,−190) Mpcredshiftof 0.09 (+0.03,−0.04).2σ

•improved constraints on stellar populations and on deviations from general relativity.

2016年6月15日宣布二探 Announcement of

second detection

Advanced LIGO第一次观测时期：

2015.9.12—2016.1.19 (51.5天-2 detectors/130天)

O1: 48.6天; PyCBC 46.1天; GstLAL 48.3天

Amplitude spectral density and Wave forms

of 3 detected signals

GW170814

—

• 2017 诺贝尔物理奖发表啰，得奖者是 85 岁的莱纳·魏 斯（Rainer Weiss）、77 岁的基普·索恩（Kip S.

Thorne）、81 岁的巴瑞·巴利许（Barry Barish），他 们因为 LIGO 探测器及重力波探测的成就而获奖，三人 将共享高达 900 万瑞典克朗（约 3,346 万元台币）的 奖金。

GW170817

中子双星合生

GW170817 中子双星合生

多信使天文学观测

引力波与伽玛暴

GRB170817A 比 GW170817 晚1.74 ± 0.05秒到达地球 重力波速度和光速相同的

精度

-310^-15  (v_/cEM)  710^-16

黑洞大小分类 Massive Black Hole Systems:

Massive BH Mergers &

Extreme Mass Ratio Mergers (EMRIs)

• 恒星质量黑洞Stellar-mass BHs (3M

< MBH ≤ 100M

)

• 超大质量黑洞Supermassive BHs (SMBHs; MBH ≥ 10

M

)

• 中级质量黑洞Intermediate-mass BHs (IMBHs; 100M

<

MBH < 10

M

)

Scope: Goals –GW Astronomy & Fundamental Physics

Frequency band GW sources / Possible GW sources Detection method Ultrahigh frequency band:

above 1 THz

Discrete sources, Cosmological sources, Braneworld Kaluza-Klein (KK) mode radiation, Plasma instabilities

Terahertz resonators, optical resonators, and magnetic conversion detectors

Very high frequency band:

100 kHz – 1 THz

Discrete sources, Cosmological sources, Braneworld Kaluza-Klein (KK) mode radiation, Plasma instabilities

Microwave resonator/wave guide detectors, laser interferometers and Gaussian beam detectors

High frequency band (audio band)*: 10 Hz – 100 kHz

Compact binaries [NS (Neutron Star)-NS, NS-BH (Black Hole), BH-BH], Supernovae

Low-temperature resonators and Earth- based laser-interferometric detectors

Middle frequency band:

0.1 Hz – 10 Hz

Intermediate mass black hole binaries, massive star (population III star) collapses

Space laser-interferometric detectors of arm length 1,000 km − 60,000 km

Low frequency band (milli-Hz band)^†: 100 nHz – 0.1 Hz

Massive black hole binaries, Extreme mass ratio inspirals (EMRIs), Compact binaries

Space laser-interferometric detectors of arm length longer than 60,000 km

Very low frequency band (nano-Hz band): 300 pHz – 100 nHz

Supermassive black hole binary (SMBHB) coalescences, Stochastic GW background from SMBHB coalescences

Pulsar timing arrays (PTAs) Ultralow frequency band: 10

fHz – 300 pHz

Inflationary/primordial GW background,

Stochastic GW background Astrometry of quasar proper motions Extremely low (Hubble)

frequency band: 1 aHz–10 fHz Inflationary/primordial GW background Cosmic microwave background experiments

Beyond Hubble-frequency

Inflationary/primordial GW background Through the verifications of primordial

2017/11/21 Taida brief history & GW Spectrum 29

引力波谱分类 The Gravitation-Wave (GW) Spectrum Classification

Cosmic band slow-roll model r=0.07, n _t =-r/8

Normalized GW spectral energy density 

vs. frequency for

GW detector sensitivities and GW sources

Very low frequency band (300 pHz – 100 nHz)

h

(f) = A

[f/(1 yr

)]

Conversion factors among:

the characteristic strain h

(f),

the strain psd (power spectral density) [S

(f)]

the normalized spectral energy density Ω

(f)

• h_c(f) = f^1/2 [S_h(f)]^1/2;

• normalized GW spectral energy density Ω_g(f): GW spectral energy density in terms of the energy density per logarithmic frequency interval divided by the cosmic closure density ρ_c for a cosmic GW sources or background, i.e.,

• Ω_gw(f) = (f/ρ_c) dρ(f)/df

• Ω_gw(f) = (2²/3H₀²) f³ S_h(f) = (2²/3H₀²) f² h_c²(f).

Strain power spectral density (psd) amplitude vs. frequency for

various GW detectors and GW sources

Characteristic strain h_c vs. frequency for various GW detectors and sources. [QA: Quasar Astrometry; QAG: Quasar Astrometry Goal; LVC: LIGO-Virgo Constraints; CSDT: Cassini Spacecraft Doppler Tracking; SMBH-GWB: Supermassive Black Hole-GW Background.]

Strain power spectral density (psd) amplitude vs.

frequency for various GW detectors and GW sources

GW20150914 LIGO

LISA

Middle frequency GW Detection Science Goals

• The science goals are the detection of GWs from

• (i) Intermediate-Mass Black Holes; could detect IMBH binaries at a few billion light years away or further

• (ii) Galactic Compact Binaries as well as stellar mass BH binaries, like GW150914;

• (iii) could alert laser interferometers days before merger by detecting inspiral phase and predict time of binany black hole coalescence & neutron star

coalescence for ground interferometers

• (iv) Relic/Inflationary GW Background.

 Analyzed three detector options:

1. Atom-laser interferometer

2. TOBA with laser interferometer 3. Michelson interferometer

 Would be astrophysically interesting, if one can reach S ^½(f ) = 10^20 Hz^1/2

Proposed Detection Methods for Middle-frequency GWs

• TOBA – The torsion bar antenna

• SOBRO -- Superconducting Omni-directional Gravitational Radiation Observatory

• Michelson Interferometer on Earth and in space

• Atom Interferometry involving repeatedly imprinting the phase of optical field onto the motional degrees of freedom of the

atoms using light propagating back and forth between the spacecraft.

• Resonant Atom Interferometry detection

• Radio-wave Doppler frequency tracking

• GW detection with optical lattice atomic clocks

 TOBA – The torsion bar

antenna; PRL2010, PRD2013

 10 m x 0.6 m ϕ quartz/Al 5056

 10 ton each

 Fundamental torsion frequency 30 μHz

Newtonian Noise –

It is uncertain whether sufficiently sensitive seismic and infrasound sensors can be

provided. It will be very challenging to achieve sufficient NN subtraction. A suppression of the NN by about 4 or 5 orders of magnitude at 0.1 Hz would be needed to make it comparable to the instrument noise limit. A larger number of more sensitive sensors will be required.

SOGRO (Paik et al 2016)

(Superconducting Omni-directional Gravitational Radiation Observatory)

A design concept that could reach a strain sensitivity of 10⁻¹⁹–10⁻²⁰ Hz^−1/2 at 0.2–10 Hz

the range of the WD–WD binary from 0.1 Hz for one year with a SNR of 10 is 1.2 Mpc, assuming one solar mass (M◉) for the WD mass.

Within this horizon, there are two massive galaxies: the Milky Way

Galaxy and Andromeda (M31). The WD–WD merger rate of ∼1.4×10⁻¹³ yr⁻¹M_◉⁻¹ has been estimated, corresponding to 0.01 per year for our Galaxy. With M31 about 0.03 per year. Probability of finding a WD–WD binary merger during one-year operation of SOGRO is ∼30% since each event is expected to persist for ∼10 years in the detector.

Binary mergers composed of IMBHs can be detected by

SOGRO up to several Gpc (see figure 1). The estimated rates of mergers are very uncertain, but up to a few tens of IMBH

Each test mass M 5 ton Nb square tube Arm length L 30-50 m Over a ‘rigid’ platform

Space GW Detection Science Goals

• The science goals are the detection of GWs from

• (i) Supermassive Black Holes;

• (ii) Extreme-Mass-Ratio Black Hole Inspirals;

• (iii) Intermediate-Mass Black Holes;

• (iv) Galactic Compact Binaries;

• (v) Detecting inspiral phase and predict time of binary

• (vi) Relic/Inflationary GW Background.

空间引力波探测

A Compilation of GW Mission Proposals LISA Pathfinder

Launched on December 3, 2015

太极

Strain power spectral density (psd) amplitude vs. frequency for various GW detectors and GW sources. [CSDT: Cassini Spacecraft Doppler

Tracking; SMBH-GWB: Supermassive Black Hole-GW Background.]

24-hr Global Campaign arXiv:1509.05446

10^6-10^6 BH-BH@10Gpc Last 3 years

AMIGO

Second Generation GW Mission Concepts

• DECIGO

• BBO

• Super-ASTROD

10^(-15) Source-Observation Gap largely bridged

• In 1915, white dwarf already discovered, the technology reached 10^(-5). First artificial satellite Sputnik launched in 1957.

• First GW space mission proposed in public in 1981 by Faller & Bender

• LISA proposed as a joint ESA-NASA mission; LISA Pathfinder

successfully performed. The drag-free tech is fully demonstrated paving the road for GW space missions.

92 days 1440 orbits 83.60 kg mass

Weak-light phase locking and manipulation technology

• Weak-light phase locking is crucial for long-distance space

interferometry and for CW laser space communication. For LISA of arm length of 5 Gm (million km) the weak-light phase locking

requirement is for 70 pW laser light to phase-lock with an onboard laser oscillator. For ASTROD-GW arm length of 260 Gm (1.73 AU) the weak-light phase locking requirement is for 100 fW laser light to lock with an onboard laser oscillator.

• Weak-light phase locking for 2 pW laser light to 200 μW local oscillator is demonstrated in our laboratory in Tsing Hua U.

• Dick et al.

from their phase-locking experiment showed a PLL (Phase

The present laser stability (16 orders) alone does not meet the GW strain sensitivity requirement (21 orders)

• For space laser-interferometric GW antenna, the arm lengths vary according to solar system orbit dynamics.

• In order to attain the requisite sensitivity, laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc.

• For suppressing laser frequency noise, it is necessary to use TDI in the analysis to match the optical path length of different beam paths closely.

• The better match of the optical path lengths is, the better cancellation of the

laser frequency noise and the easier to achieve the requisite sensitivity. In

case of exact match, the laser frequency noise is fully canceled, as in the

original Michelson interferometer.

AMIGO: Astrodynamical Middle-frequency Interferometric GW Observatory

• Arm length: 10,000 km (or a few times)

• Laser power: 2-10 W (or more)

• Acceleration noise: assuming LPF noise

• Orbit: 4 options (all LISA-like formations):

(i) Earth-like solar orbit (3-20 degrees behind the Earth orbit) (ii) 600,000 km high orbits around the

(iii) 100,000 km-250,000 high orbits around the Earth (iv) near Earth-Moon L4 and L5 orbits

• Scientific Goal: to bridge the gap between high-frequency and low-

frequency GW sensitivities. Detecting intermediate mass BH coalescence.

GW Sensitivities of AMIGO

• Baseline Sensitivity: 2 W emitting laser power, 300 mm φ telescope

•

• over the frequency range of 20 μHz < f < 1 kHz. Here L

= 0.01 × 10

m is the AMIGO arm length, f

= c/(2πL

) is the AMIGO arm transfer frequency, S

= 1.424 × 10

m

Hz

is the (white) position noise level due to laser shot noise which is 16 × 10

(=0.004

) times that for new LISA.

S

(f) is the same colored acceleration noise level in (2)

• Design Sensitivity: 10 W emitting laser power, 360 mm φ telescope Shot noise for strain to gain a factor of

10 [ (10W/2W)×(360mm/300mm)

]

AMIGO solid curve by using S

= 0.1424 × 10

m

Hz

.

LISA 2.5 Gm Sensitivity

• The new LISA design sensitivity is in [10, 11]. A simple analytical approximation of the design sensitivity is in Petiteau et al. [10] and used by Cornish and Robson [26]:

• S•_Ln^1/2(f) = (20/3)^1/2 (1/L_L) × [(1 + (f / (1.29f_L))² )]^1/2 × [(S_Lp + 4S_a/(2πf)⁴)]^1/2 Hz^−1/2, (1)

•

• over the frequency range 20 μHz < f < 1 Hz. Here L_L = 2.5 Gm is the LISA arm length, f_L

= c / (2πL_L) is the LISA arm transfer frequency, S_Lp = 8.9 × 10⁻²³ m² Hz^-1 is the white position noise, and

•

• S_a(f) = 9 × 10⁻³⁰ [1 + (10^4 Hz/ f )² + 16 (2 × 10^5 Hz/ f )¹⁰ ] m² s^4 Hz^1, (2)

Orbit design: Earth-like solar orbits

T

D

I

Time Delay Interferometry

Space Detection Methods other than Laser Interferometry

for Low-frequency and Middle-frequency GWs

• Radio-wave Doppler frequency tracking

• Atom Interferometry involving repeatedly imprinting the phase of optical field onto the motional degrees of

freedom of the atoms using light propagating back and forth between the spacecraft.

• Resonant Atom Interferometry detection

Summary

• Success of Interferometric Detection of GW

• Stellar-size BH distribution is largely set by observation

• Multi-Messenger Astronomy is started bright

• GW spectrum and detection sensitivities are presented

• Cosmic Band, Quaser Astrometry Band and PTA band

• Space GW detection, new LISA and Super-ASTROD and AMIGO, Middle-Frequency Band

• GW and Multi-Messenger Astronomy: Focus of Next 50 yrs