Sensitivity studies for third-generation gravitational wave observatories
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IOP PUBLISHING CLASSICAL AND QUANTUM GRAVITY
Class. Quantum Grav. 28 (2011) 094013 (13pp) doi:10.1088/0264-9381/28/9/094013
Sensitivity studies for third-generation gravitational
wave observatories
S Hild
1
, M Abernathy
1
, F Acernese
2,3
, P Amaro-Seoane
4,5
,
N Andersson
6
, K Arun
7
, F Barone
2,3
, B Barr
1
, M Barsuglia
8
,MBeker
9
,
N Beveridge
1
, S Birindelli
10
,SBose
11
,LBosi
12
, S Braccini
13
,
C Bradaschia
13
, T Bulik
14
, E Calloni
2,15
, G Cella
13
,
E Chassande Mottin
8
, S Chelkowski
16
, A Chincarini
17
, J Clark
18
,
E Coccia
19,20
, C Colacino
13
,JColas
21
, A Cumming
1
, L Cunningham
1
,
E Cuoco
21
, S Danilishin
22
, K Danzmann
23
, R De Salvo
24
, T Dent
18
,
RDeRosa
2,15
,LDiFiore
2,15
, A Di Virgilio
13
, M Doets
25
, V Fafone
19,20
,
P Falferi
26
, R Flaminio
27
, J Franc
27
, F Frasconi
13
,AFreise
16
,
D Friedrich
23
,PFulda
16
,JGair
28
, G Gemme
17
, E Genin
21
, A Gennai
16
,
A Giazotto
13,21
, K Glampedakis
29
,CGr
¨
af
23
, M Granata
8
,HGrote
23
,
G Guidi
30,31
, A Gurkovsky
22
, G Hammond
1
, M Hannam
18
, J Harms
24
,
D Heinert
32
, M Hendry
1
, I Heng
1
, E Hennes
9
, J Hough
2
,SHusa
33
,
S Huttner
1
, G Jones
18
, F Khalili
22
, K Kokeyama
16
, K Kokkotas
29
,
B Krishnan
4
,TGFLi
9
, M Lorenzini
30
,HL
¨
uck
23
, E Majorana
34
,
I Mandel
35
, V Mandic
36
, M Mantovani
13
, I Martin
1
, C Michel
27
,
Y Minenkov
19,20
, N Morgado
27
, S Mosca
2,15
, B Mours
37
,
HM
¨
uller–Ebhardt
23
, P Murray
1
, R Nawrodt
1,32
,JNelson
1
,
R Oshaughnessy
38
,CDOtt
39
,CPalomba
34
, A Paoli
21
, G Parguez
21
,
A Pasqualetti
21
, R Passaquieti
13,40
, D Passuello
13
, L Pinard
27
,
W Plastino
41
, R Poggiani
13,40
, P Popolizio
21
, M Prato
17
, M Punturo
12,21
,
P Puppo
34
, D Rabeling
9,25
, P Rapagnani
34,42
, J Read
43
, T Regimbau
10
,
H Rehbein
23
,SReid
1
, F Ricci
34,42
, F Richard
21
, A Rocchi
19
, S Rowan
1
,
AR
¨
udiger
23
, L Santamar
´
ıa
24
, B Sassolas
27
, B Sathyaprakash
18
,
R Schnabel
23
, C Schwarz
32
, P Seidel
32
, A Sintes
33
, K Somiya
39
,
F Speirits
1
, K Strain
1
, S Strigin
22
, P Sutton
18
, S Tarabrin
23
,
ATh
¨
uring
23
, J van den Brand
9,25
, M van Veggel
1
, C van den Broeck
9
,
A Vecchio
16
,JVeitch
18
, F Vetrano
30,31
, A Vicere
30,31
, S Vyatchanin
22
,
B Willke
23
, G Woan
1
and K Yamamoto
44
1
SUPA, School of Physics and Astronomy, The University of Glasgow, Glasgow, G12 8QQ, UK
2
INFN, Sezione di Napoli, Italy
3
Universit
`
a di Salerno, Fisciano, I-84084 Salerno, Italy
4
Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am M
¨
uhlenberg 1,
D-14476 Potsdam, Germany
5
Institut de Ci
`
encies de l’Espai (CSIC-IEEC), Campus UAB, Torre C-5, parells, 2
na
planta,
ES-08193, Bellaterra, Barcelona, Spain
6
University of Southampton, Southampton SO17 1BJ, UK
7
LAL, Universit
´
e Paris-Sud, IN2P3/CNRS, F-91898 Orsay, France
8
AstroParticule et Cosmologie (APC), CNRS; Observatoire de Paris, Universit
´
e Denis Diderot,
Paris VII, France
9
Nikhef, Science Park 105, 1098 XG Amsterdam, The Netherlands
0264-9381/11/094013+13$33.00 © 2011 IOP Publishing Ltd Printed in the UK & the USA 1
Class. Quantum Grav. 28 (2011) 094013 S Hild et al
10
Universit
´
e Nice ‘Sophia–Antipolis’, CNRS, Observatoire de la C
ˆ
ote d’Azur, F-06304 Nice,
France
11
Washington State University, Pullman, WA 99164, USA
12
INFN, Sezione di Perugia, I-6123 Perugia, Italy
13
INFN, Sezione di Pisa, Italy
14
Astronomical Observatory, University of warsaw, Al Ujazdowskie 4, 00-478 Warsaw, Poland
15
Universit
`
a di Napoli ‘Federico II’, Complesso Universitario di Monte S. Angelo, I-80126
Napoli, Italy
16
University of Birmingham, Birmingham, B15 2TT, UK
17
INFN, Sezione di Genova, I-16146 Genova, Italy
18
Cardiff University, Cardiff, CF24 3AA, UK
19
INFN, Sezione di Roma Tor Vergata I-00133 Roma, Italy
20
Universit
`
a di Roma Tor Vergata, I-00133, Roma, Italy
21
European Gravitational Observatory (EGO), I-56021 Cascina (Pi), Italy
22
Moscow State University, Moscow, 119992, Russia
23
Max–Planck–Institut f
¨
ur Gravitationsphysik and Leibniz Universit
¨
at Hannover, D-30167
Hannover, Germany
24
LIGO, California Institute of Technology, Pasadena, CA 91125, USA
25
VU University Amsterdam, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands
26
INFN, Gruppo Collegato di Trento, Sezione di Padova; Istituto di Fotonica e Nanotecnologie,
CNR-Fondazione Bruno Kessler, I-38123 Povo, Trento, Italy
27
Laboratoire des Mat
´
eriaux Avanc
´
es (LMA), IN2P3/CNRS, F-69622 Villeurbanne, Lyon,
France
28
University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
29
Theoretical Astrophysics (TAT) Eberhard-Karls-Universit
¨
at T
¨
ubingen, Auf der Morgenstelle
10, D-72076 T
¨
ubingen, Germany
30
INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Italy
31
Universit
`
a degli Studi di Urbino ‘Carlo Boapos;, I-61029 Urbino, Italy
32
Friedrich–Schiller–Universit
¨
at Jena PF, D-07737 Jena, Germany
33
Departament de Fisica, Universitat de les Illes Balears, Cra. Valldemossa Km. 7.5, E-07122
Palma de Mallorca, Spain
34
INFN, Sezione di Roma 1, I-00185 Roma, Italy
35
Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA
36
University of Minnesota, Minneapolis, MN 55455, USA
37
LAPP-IN2P3/CNRS, Universit
´
e de Savoie, F-74941 Annecy-le-Vieux, France
38
The Pennsylvania State University, University Park, PA 16802, USA
39
Caltech–CaRT, Pasadena, CA 91125, USA
40
Universit
`
a di Pisa, I-56127 Pisa, Italy
41
INFN, Sezione di Roma Tre and Universit
`
a di Roma Tre, Dipartimento di Fisica, I-00146
Roma, Italy
42
Universit
`
a ‘La Sapienza’, I-00185 Roma, Italy
43
University of Mississippi, MS38677, USA
44
INFN, sezione di Padova, via Marzolo 8, 35131 Padova, Italy
E-mail: stefan.hild@glasgow.ac.uk
Received 4 December 2010, in final form 7 January 2011
Published 18 April 2011
Online at stacks.iop.org/CQG/28/094013
Abstract
Advanced gravitational wave detectors, currently under construction, are
expected to directly observe gravitational wave signals of astrophysical origin.
The Einstein Telescope (ET), a third-generation gravitational wave detector,
has been proposed in order to fully open up the emerging field of gravitational
wave astronomy. In this paper we describe sensitivity models for ET and
investigate potential limits imposed by fundamental noise sources. A special
focus is set on evaluating the frequency band below 10 Hz where a complex
2
Class. Quantum Grav. 28 (2011) 094013 S Hild et al
mixture of seismic, gravity gradient, suspension thermal and radiation pressure
noise dominates. We develop the most accurate sensitivity model, referred
to as ET-D, for a third-generation detector so far, including the most relevant
fundamental noise contributions.
PACS numbers: 04.80.Nn, 95.75.Kk
(Some figures in this article are in colour only in the electronic version)
1. Introduction
The currently operating gravitational wave (GW) detectors LIGO [1], Virgo [2], GEO 600
[3] and TAMA [4] are based on extremely sensitive Michelson interferometers. While the
sensitivity achieved by these first-generation detectors is mainly limited by shot noise, mirror
thermal noise and seismic noise, for the second generation of instruments, such as Advanced
LIGO [5], Advanced Virgo [6], GEO-HF [7] and LCGT [8], additional fundamental noise
sources will start to play a role toward the low-frequency end of the detection band: thermal
noise of the test mass suspension, photon radiation pressure noise and seismically driven
gravity gradients acting on the test masses. These three sources of noise will become even
more important for third-generation GW observatories such as the Einstein Telescope (ET)
[9, 10], as these detectors aim to significantly increase the detection band toward frequencies
aslowasafewHz[11, 13]. Therefore, major parts of the ET design are driven by exactly
these noise sources. An overview of the importance of the sub-10 Hz band for astrophysical
and cosmological analyses can be found in [9].
In this paper we will give an overview of the currently ongoing ET design activities
with a special focus on the modelling of the achievable sensitivity taking the most important
fundamental noise sources into account. The first sensitivity estimate for a third-generation
interferometer was described in [11, 12] and was based on a single interferometer covering the
full frequency range from about 1 Hz to 10 kHz. In the following we will refer to this sensitivity
curve as ET-B. Subsequently we developed a more realistic design, taking cross-compatibility
aspects of the various involved technologies into account. This led to the so-called xylophone
design, in which one GW detector is composed of two individual interferometers: A low-power
cryogenic low-frequency interferometer and a high-power room temperature high-frequency
interferometer. A detailed description of this xylophone detector sensitivity, in the following
referred to as ET-C, can be found in [13]. The ET-C configuration will serve as a starting
point for the investigations described in this paper. We improved the sensitivity models
for ET by including additional new noise sources as well as by amending and updating noise
contributions already previously included. These improvements, which led to a new sensitivity
estimate, referred to as ET-D, will be presented and discussed in this paper.
In section 2 we discuss seismic and gravity-gradient noise, followed by the quantum-noise
contribution in section 3. Thermal noise of the suspensions and test masses will be presented
in section 4. An improved noise budget for ET is then given in section 5. We conclude with a
brief overview of the configuration of a full third-generation observatory, consisting of several
GW detectors.
2. Seismic isolation and gravity-gradient noise
Seismic noise couples into the differential arm length of a GW detector via two main paths.
First of all, seismic excitation can mechanically couple through the suspension and seismic
3
Class. Quantum Grav. 28 (2011) 094013 S Hild et al
10
−1
10
0
10
1
10
−12
10
−11
10
−10
10
−9
10
−8
10
−7
10
−6
Frequency [Hz]
Seismic displacement [m/sqrt(Hz)]
Black Forest (BFO),
12.9.2010
10
−1
10
0
10
1
10
−20
10
−15
10
−10
10
−5
10
0
Frequency [Hz]
Tranferfunction
Superattenuator,
17m, 6 stages
10
0
10
1
10
−25
10
−24
10
−23
10
−22
10
−21
Frequency [Hz]
Strain [1/sqrt(Hz)]
ET−B total noise
ET−C total noise
Seismic noise
(50m suspension)
Seismic noise
(17m suspension +
Blackforest seismic)
Figure 1. Seismic noise spectrum from an underground location in the Black Forest, Germany
(left-hand panel). Transfer function of a superattenuator consisting of six stages with an overall
height of 17 m (center panel). The right-hand panel shows the resulting seismic noise contribution
for the 17 m superattenuator for the seismic excitation at the Black Forest site (green dashed line).
For comparison ET-B and ET-C are also plotted. Their seismic noise contribution is based on the
assumption of a generic five-stage 50 m suspension.
isolation systems. Second, seismic noise excites density fluctuations in the environment of
the GW detector, which couple via gravitational attraction to the test-mass position. In the
following we will refer to these two noise sources as seismic noise and gravity-gradient noise,
respectively. The main difference between these two noise sources is that while seismic noise
can be reduced by application of complex seismic isolation systems, the only guaranteed way
to reduce the gravity-gradient noise is to reduce the initial seismic excitation.
45
Therefore,
third-generation GW detectors are proposed to be built in quiet underground locations.
The seismic noise contribution of the low-frequency interferometer of ET-C was based on
a seismic excitation of 5 × 10
−9
m/
√
Hz/f
2
(where f is the frequency in Hz) and a generic
50 m tall seismic isolation system consisting of five passive pendulum stages, each of 10 m
height. A more realistic seismic isolation design, based on the Virgo superattenuator concept
[14, 15], has been developed recently [16]. To achieve a lower cut-off frequency the height
of the individual pendulum stages of the superattenuator will be extended to 2 m per stage.
The overall isolation of the proposed modified superattenuator, consisting of six pendulum
stages (each stage providing horizontal as well as vertical isolation) and a total height of
17 m, is shown in the center panel of figure 1. Using the seismic excitation level, measured
in an underground facility of the Black Forest Observatory (BFO) [17, 18], shown in the left
panel of figure 1, we can derive the expected seismic noise contribution to the ET noise budget.
The result is shown in the right-hand panel of figure 1. Reducing the height of the seismic
isolation system from 50 to 17 m increases the cut-off frequency only slightly from about 1.2
to 1.7 Hz.
Gravity-gradient noise has been described in detail [20–22]. In our simulations we
estimate the power spectral density of the gravity-gradient noise contribution as
N
GG
(f )
2
=
4 · β
2
· G
2
· ρ
2
r
L
2
· f
4
· X
2
seis
, (1)
45
Many promising gravity-gradient noise subtraction schemes have been suggested in the literature [19]. However,
as none of these schemes has been demonstrated so far, we do not consider them in this paper.
4
![Figure 2. Left panel: gravity-gradient noise contribution to ET, for various β values, assuming the BFO spectrum shown in figure 1 as the seismic excitation level. Right panel: suspension thermal noise of the low-frequency interferometer of ET as described in [34].](/figures/figure-2-left-panel-gravity-gradient-noise-contribution-to-866ijshm.webp)
![Figure 6. Historical evolution of sensitivity models for the Einstein Telescope, starting from a single cryogenic broadband detector (ET-B) [11], over the initial xylophone design (ET-C) [13] to the ET-D sensitivity described in this paper.](/figures/figure-6-historical-evolution-of-sensitivity-models-for-the-1gp0ige0.webp)
![Figure 3. Left panel: simplified schematic of an ET interferometer. Quantum-noise suppression is achieved by the injection of squeezed light states with a frequency-dependent squeezing angle. The frequency-dependent rotation of the squeezing angle can be realized by using the dispersion of filter cavities, on which the squeezed light is reflected. Each ET low-frequency interferometer will require two filter cavities, while each high-frequency interferometer only requires a single filter cavity. Right-hand panel: quantum-noise contribution of the ET low-frequency interferometer, as described in [13] (dashed line) and with squeezing losses from filter cavities taken into account (solid line) [27].](/figures/figure-3-left-panel-simplified-schematic-of-an-et-2a1vqp2v.webp)
