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July 26, 2019 TianQin Summer School 2019 @ Sun Yat-sen University Laser Interferometry for Gravitational Wave Observations 3. Sensitivity Design Yuta Michimura Department of Physics, University of Tokyo Contents 1. Laser Interferometers

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Laser Interferometry for Gravitational Wave Observations

  • 3. Sensitivity Design

Yuta Michimura

Department of Physics, University of Tokyo

TianQin Summer School 2019 @ Sun Yat-sen University July 26, 2019

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SLIDE 2

Contents

2

  • 1. Laser Interferometers (July 25 PM)

Michelson interferometer Fabry-Pérot interferometer

  • 2. Quantum Noise (July 25 PM)

Shot noise and radiation pressure noise Standard quantum limit

  • 3. Sensitivity Design (July 26 AM)

Force noise and displacement noise Inspiral range and time to merger Space interferometer design

  • 4. Status of KAGRA (July 26 AM)

Status of KAGRA detector in Japan Future prospects

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SLIDE 3

Review on Quantum Noise

3

Fabry-Pérot-Michelson (100 W, Finesse 100) Michelson (100 W) Dependent only on input power Heavier and longer the better Cavity pole

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SLIDE 4

Low Frequency Noises

  • We have shown that the designed sensitivity of

current/proposed GW detectors are mostly determined by quantum noise

  • But there are other classical noises at low

frequencies

4

TianQin Shot noise

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SLIDE 5

Force Noises

  • There are many kinds of force noises (acceleration

noises)

  • Contribution of force noises to strain sensitivity
  • Longer arm

is better

5

  • D. Bortoluzzi+, CQG 21, S573 (2004)
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SLIDE 6

Force Noise Requirements

  • B-DECIGO requirement is most stringent due to

shorter arm length

6

B-DECIGO LISA TianQin

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SLIDE 7

LISA Pathfinder Acceleration Noise

  • 2e-15 m/sec2/√Hz achieved, which correspond to

4e-15 N/√Hz for 2 kg test mass

7

  • M. Armano+, PRL 120, 061101 (2018)
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SLIDE 8

Design Comparison

8

LISA TianQin B-DECIGO

Arm length 2.5e6 km 1.7e5 km 100 km Interferometry Optical transponder Optical transponder Fabry-Pérot cavity Laser frequency stabilization Reference cavity, 1064 nm Reference cavity, 1064 nm Iodine, 515 nm Orbit Heliocentric Geocentric, facing

J0806.3+1527

Geocentric (TBD) Flight configuration Constellation flight Constellation flight Formation flight Test mass 1.96 kg 2.45 kg 30 kg Force noise req. 8e-15 N/rtHz Achieved

PRL 120, 061101 (2018)

7e-15 N/rtHz

CQG 33, 035010 (2016)

1e-16 N/rtHz

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SLIDE 9

DECIGO Design

  • To be sensitive to 0.1-10 Hz band, shorter arm is

required

  • DECIGO chose to do Fabry-Pérot to be sensitive in

0.1-10 Hz band, which requires large mirrors (and short arm) to form a cavity

  • Low frequency noise should be

limited by quantum radiation pressure noise (if limited by

classical force noise, higher power would be preferable in terms of horizon distance)

9

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SLIDE 10

Horizon Distance

  • One of the figures of merit of gravitational wave

detectors is detectable distance of compact binary coalescences

  • Maximum signal to noise ratio of inspiral signal can

be calculated with

10

Luminosity distance Detector sensitivity Chirp mass

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SLIDE 11

Horizon Distance

  • If we set the SNR threshold, maximum luminosity

distance can be calculated for given chirp mass

  • We usually set
  • Chirp mass used below is detector frame mass

11

Luminosity distance Detector sensitivity Chirp mass

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SLIDE 12

Sensitivity Curves of GW Detectors

12

B-DECIGO LISA

Cosmic Explorer Einstein Telescope aLIGO KAGRA

LISA: https://perf-lisa.in2p3.fr/ TianQin: arXiv:1902.04423 (from Yi-Ming Hu) B-DECIGO: PTEP 2016, 093E01 (2016) KAGRA: PRD 97, 122003 (2018) aLIGO: LIGO-T1800044 ET: http://www.et-gw.eu/index.php/etdsdocument CE: CQG 34, 044001 (2017)

TianQin

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SLIDE 13

Horizon Distance Comparison

13

B-DECIGO LISA TianQin

CE ET aLIGO GW150914 GW170817

Optimal direction and polarization SNR threshold 8

z=10 z=1

KAGRA

O1 and O2 binaries plotted

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SLIDE 14

Horizon Distance Comparison

14

B-DECIGO LISA TianQin

CE ET aLIGO GW150914 GW170817

Optimal direction and polarization SNR threshold 8

z=10 z=1

KAGRA

O1 and O2 binaries plotted

Neutron Stars Stellar-Mass Black Holes Intermediate-Mass Black Holes Supermassive Black Holes

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SLIDE 15

Inspiral Signal

  • in amplitude spectrum density, upto around

GW frequency at innermost stable circular orbit

15

B-DECIGO LISA

CE ET aLIGO KAGRA

TianQin

  • 7/3*1/2+1/2=-2/3
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SLIDE 16

Inspiral Signal and SQL

  • SQL follows , so higher SQL touching frequency

gives larger inspiral range, as long as inspiral signal is in the detector band

16

B-DECIGO LISA

aLIGO KAGRA

TianQin

CE ET

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SLIDE 17

SQL Touching Frequency

  • Quantum noise touches SQL where
  • When (frequency below cavity pole) ,
  • Higher power is required for higher SQL touching frequency

17

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SLIDE 18

Time to Merger

  • Time it takes to merger from a certain GW frequency

18

year month day hour

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SLIDE 19

Time to Merger and Detector Band

  • Different observation band sees different phases

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B-DECIGO LISA TianQin

aLIGO CE ET

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SLIDE 20

Time to Merger and Detector Band

  • Different observation band sees different phases

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B-DECIGO LISA TianQin

aLIGO KAGRA CE ET

all @ z=3 (26 Gpc)

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SLIDE 21

Detector Design Example 1

  • What will be the detector design if you want to

detect 105Msun-105Msun merger at the highest signal to noise ratio?

  • Assume 100 km arms with 30 kg mirrors

21

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SLIDE 22

Detector Design Example 1

  • What will be the detector design if you want to

detect 105Msun-105Msun merger at the highest signal to noise ratio?

  • Assume 100 km arms with 30 kg mirrors

22

Let’s simplify and consider detector frame mass Also, consider SNR at ISCO frequency These give you SQL

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SLIDE 23

Detector Design Example 1

  • What will be the detector design if you want to

detect 105Msun-105Msun merger at the highest signal to noise ratio?

  • Assume 100 km arms with 30 kg mirrors

23

Let’s simplify and consider detector frame mass Also, consider SNR at ISCO frequency These give you SQL We want to reach SQL at ISCO frequency (1064 nm) FP case

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SLIDE 24

Detector Design Example 1

  • What will be the detector design if you want to

detect 105Msun-105Msun merger at the highest signal to noise ratio?

  • Assume 100 km arms with 30 kg mirrors

24

Let’s simplify and consider detector frame mass Also, consider SNR at ISCO frequency These give you SQL We want to reach SQL at ISCO frequency

* Infinite mass BS assumed

(1064 nm) Michelson case

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SLIDE 25

Detector Design Example 1

25

FP P0=0.09 W F=10 Michelson P0=7.3W

SNR

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SLIDE 26

Detector Design Example 1

  • What will be the detector design if you want to

detect 105Msun-105Msun merger at the highest signal to noise ratio?

  • Assume 100 km arms with 30 kg mirrors

26

Actually, force noise requirement will be quite severe with this configuration To relax this requirement, it is better to increase the arm length at the cost of reducing the power LISA and TianQin design

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SLIDE 27

Detector Design Example 2

  • What will be the detector design if you want to

detect GW170817 a month before the merger?

  • Assume 10 km arms with 2 kg mirrors

27

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SLIDE 28

Detector Design Example 2

  • What will be the detector design if you want to

detect GW170817 a month before the merger?

28

Force noise we want 8.4e-22 /f2 /√Hz Shot noise less than 2.4e-21 /√Hz

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SLIDE 29

Detector Design Example 2

  • What will be the detector design if you want to

detect GW170817 a month before the merger?

29

The force noise requirement will be With Michelson configuration, laser power requirement will be Even larger power required for more SNR

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SLIDE 30

Detector Design Example 2

  • What will be the detector design if you want to

detect GW170817 a month before the merger?

30

If FP configuration, power requirement will be relaxed Input power of 1.6 W Finesse of 100 will do Force noise requirement stays the same

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SLIDE 31

Detector Design Example 2

  • What will be the detector design if you want to

detect GW170817 a month before the merger?

31

Michelson P0=60W > 6 W req. Classical force noise 6.6e-16 N/√Hz FP P0=1.6 W F=100

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SLIDE 32

Detector Design Example 3

  • What will be the detector design if you want to have

the maximum SNR for inspiral of GW170817?

  • Assume 3 km arms and 20 kg mirrors

32

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SLIDE 33

Detector Design Example 3

  • What will be the detector design if you want to have

the maximum SNR for inspiral of GW170817?

33

Shot noise at high frequency should be less than 8.8e-27*f /√Hz SQL touching frequency should be high up to ~200 Hz

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SLIDE 34

Detector Design Example 3

  • What will be the detector design if you want to have

the maximum SNR for inspiral of GW170817?

34

If FP configuration, shot noise at high frequencies will be (Independent of L) With this power and SQL touching frequency Not possible with Michelson

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SLIDE 35

Detector Design Example 3

  • What will be the detector design if you want to have

the maximum SNR for inspiral of GW170817?

35

FP P0=1.5e4 W F=180 … or RSE P0=150 W F=1800 PRG=10 SRG=0.1

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SLIDE 36

Summary

  • Apart from quantum noise, classical force noise at

low frequency have to be considered to design a gravitational wave detector

  • Force noise requirement for Fabry-Pérot

interferometers is severer compared with optical transponder due to shorter arm

  • Different interferometer design is required for

different observation bands

  • Low frequency detectors can see heavier binary

mergers and early phases of lighter binary inspiral signals

36

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SLIDE 37

Books

  • Peter R. Saulson
  • Jolien D. E. Creighton, Warren G. Anderson
  • Michele Maggoire

37

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SLIDE 38

Further References

  • E. D. Black & R. N. Gutenkunst, American Journal of

Physics 71, 365 (2003) An introduction to signal extraction in interferometric gravitational wave detectors

  • A. Buonanno and Y. Chen, Phys. Rev. D 64, 042006 (2001)

Quantum noise in second generation, signal-recycled laser interferometric gravitational-wave detectors

  • T. Nakamura+, Progress of Theoretical and Experimental

Physics 2016, 093E01 (2016) Pre-DECIGO can get the smoking gun to decide the astrophysical or cosmological origin of GW150914-like binary black holes

  • Y. Michimura+, Phys. Rev. D 97, 122003 (2018)

Particle swarm optimization of the sensitivity of a cryogenic gravitational wave detector

38

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SLIDE 39

Slides Available Online

39

  • 1. Laser Interferometers (July 25 PM)

https://tinyurl.com/YM20190725-1

  • 2. Quantum Noise (July 25 PM)

https://tinyurl.com/YM20190725-2

  • 3. Sensitivity Design (July 26 AM)

https://tinyurl.com/YM20190725-3

  • 4. Status of KAGRA (July 26 AM)

https://tinyurl.com/YM20190725-4

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SLIDE 40

Additional Slides

40

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SLIDE 41

Multiband GW Observation

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  • A. Sesana, Phys. Rev. Lett. 116, 231102 (2016)
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SLIDE 42

Multiband GW Observation

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LISA L3 proposal https://www.elisascience.org/files/publications/LISA_L3_20170120.pdf

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SLIDE 43
  • Force noise requirement
  • Radiation pressure noise
  • If you fix requirement for , requirement for is set
  • If you fix , finesse is set
  • Assuming g-factor g=0.3 and , beam size is calculated
  • This gives you the minimum mirror mass from diffraction

loss (assume fused silica, aspect ratio t/d = 1)

  • Also, if you fix initial alignment accuracy, minimum mirror

diameter is determined from

Mirror Mass and Arm Length (FP)

43

Say, this is 3

There’s no point in reducing the finesse and input power if force noise is larger, in terms of sensitivity.

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SLIDE 44
  • cf. star tracker can do

better than 1 arcsec (~5 urad)

Mirror Mass and Arm Length (FP)

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Not allowed from force noise Not allowed from initial alignment Not allowed from diffraction loss (depends much

  • n aspect ratio)

30 kg, 3 km B-DECIGO

  • cf. GRACE-FO

launched May 2018 does 220 km FF

From SQL 10 kg, 10 km More sensitive