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Advanced gravitational wave detectors, currently under construction, are expected to directly observe gravitational wave signals of astrophysical origin. The Einstein Telescope, a third-generation gravitational wave detector, has been proposed in

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Sensitivity Studies for Third-GenerationGravitational Wave Observatories
SHild
3
, MAbernathy
3
, FAcernese
4
,
5
, PAmaro-Seoane
33
,
46
,NAndersson
7
, KArun
8
, FBarone
4
,
5
, BBarr
3
, MBarsuglia
9
,MBeker
45
, NBeveridge
3
, SBirindelli
11
, SBose
12
, LBosi
1
,SBraccini
13
, CBradaschia
13
, TBulik
14
, ECalloni
4
,
15
,GCella
13
, EChassandeMottin
9
, SChelkowski
16
,AChincarini
17
, JClark
18
, ECoccia
19
,
20
, CColacino
13
,JColas
2
, ACumming
3
, LCunningham
3
, ECuoco
2
,SDanilishin
21
, KDanzmann
6
, RDeSalvo
23
, TDent
18
,RDeRosa
4
,
15
, LDiFiore
4
,
15
, ADiVirgilio
13
, MDoets
10
,VFafone
19
,
20
, PFalferi
24
, RFlaminio
25
, JFranc
25
,FFrasconi
13
, AFreise
16
, DFriedrich
6
, PFulda
16
, JGair
26
,GGemme
17
, EGenin
2
, AGennai
16
, AGiazotto
2
,
13
,KGlampedakis
27
, CGr¨af
6
MGranata
9
, HGrote
6
,GGuidi
28
,
29
, AGurkovsky
21
, GHammond
3
, MHannam
18
,JHarms
23
, DHeinert
32
, MHendry
3
, IHeng
3
, EHennes
45
,JHough
4
, SHusa
44
, SHuttner
3
, GJones
18
, FKhalili
21
,KKokeyama
16
, KKokkotas
27
, BKrishnan
33
, T.G.F.Li
45
,MLorenzini
28
, HL¨uck
6
, EMajorana
34
, IMandel
35
,
36
,VMandic
31
, MMantovani
13
, IMartin
3
, CMichel
25
,YMinenkov
19
,
20
, NMorgado
25
, SMosca
4
,
15
, BMours
37
,HM¨uller–Ebhardt
6
, PMurray
3
, RNawrodt
3
,
32
, JNelson
3
,ROshaughnessy
38
, CDOtt
39
, CPalomba
34
, APaoli
2
,GParguez
2
, APasqualetti
2
, RPassaquieti
13
,
40
,DPassuello
13
, LPinard
25
, WPlastino
42
, RPoggiani
13
,
40
,PPopolizio
2
, MPrato
17
, MPunturo
1
,
2
, PPuppo
34
,DRabeling
10
,
45
, PRapagnani
34
,
41
, JRead
33
, TRegimbau
11
,HRehbein
6
, SReid
3
, FRicci
34
,
41
, FRichard
2
, ARocchi
19
,SRowan
3
, AR¨udiger
6
, LSantamar´ıa
23
, BSassolas
25
,BSathyaprakash
18
, RSchnabel
6
, CSchwarz
32
, PSeidel
32
,ASintes
44
, KSomiya
39
, FSpeirits
3
, KStrain
3
, SStrigin
21
,PSutton
18
, STarabrin
6
, ATh¨uring
6
, JvandenBrand
10
,
45
,MvanVeggel
3
, CvandenBroeck
45
, AVecchio
16
, JVeitch
18
,FVetrano
28
,
29
, AVicere
28
,
29
, SVyatchanin
21
, BWillke
6
,GWoan
3
, KYamamoto
30
E-mail:
stefan.hild@glasgow.ac.uk
1
INFN, Sezione di Perugia, I-6123 Perugia, Italy
2
European Gravitational Observatory (EGO), I-56021 Cascina (Pi), Italy
3
SUPA, School of Physics and Astronomy, The University of Glasgow, Glasgow,G128QQ, UK
4
INFN, Sezione di Napoli, Italy
5
Universit`a di Salerno, Fisciano, I-84084 Salerno, Italy
a r X i v : 1 0 1 2 . 0 9 0 8 v 1 [ g r - q c ] 4 D e c 2 0 1 0
Sensitivity Studies for Third-Generation Gravitational Wave Observatories
2
6
Max–Planck–Institut f¨ur Gravitationsphysik and Leibniz Universit¨atHannover, D-30167 Hannover, Germany
7
University of Southampton, Southampton SO171BJ, UK
8
LAL, Universit´e Paris-Sud, IN2P3/CNRS, F-91898 Orsay, France
9
AstroParticule et Cosmologie (APC), CNRS; Observatoire de Paris, Universit´eDenis Diderot, Paris VII, France
10
VU University Amsterdam, De Boelelaan 1081, 1081 HV, Amsterdam, TheNetherlands
11
Universit´e Nice ‘Sophia–Antipolis’, CNRS, Observatoire de la Cˆote d’Azur,F-06304 Nice, France
12
Washington State University, Pullman, WA 99164, USA
13
INFN, Sezione di Pisa, Italy
14
Astronomical Observatory, University of warsaw, Al Ujazdowskie 4, 00-478Warsaw, 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
Moscow State University, Moscow, 119992, Russia
22
INFN, Laboratori Nazionali del Gran Sasso, Assergi l’Aquila, Italy
23
LIGO, California Institute of Technology, Pasadena, CA 91125, USA
24
INFN, Gruppo Collegato di Trento, Sezione di Padova; Istituto di Fotonica eNanotecnologie, CNR-Fondazione Bruno Kessler, I-38123 Povo, Trento, Italy
25
Laboratoire des Mat´eriaux Avanc´es (LMA), IN2P3/CNRS, F-69622Villeurbanne, Lyon, France
26
University of Cambridge, Madingley Road, Cambridge, CB3 0HA, UK
27
Theoretical Astrophysics (TAT) Eberhard-Karls-Universit¨at T¨ubingen, Auf der Morgenstelle 10, D-72076 T¨ubingen, Germany
28
INFN, Sezione di Firenze, I-50019 Sesto Fiorentino, Italy
29
Universit`a degli Studi di Urbino ‘Carlo Bo’, I-61029 Urbino, Italy
30
INFN, sezione di Padova, via Marzolo 8, 35131 Padova, Italy
31
University of Minnesota, Minneapolis, MN 55455, USA
32
Friedrich–Schiller–Universit¨at Jena PF, D-07737 Jena, Germany
33
Max Planck Institute for Gravitational Physics (Albert Einstein Institute)Am M¨uhlenberg 1, D-14476 Potsdam, Germany
34
INFN, Sezione di Roma 1, I-00185 Roma, Italy
35
Department of Physics and Astronomy, Northwestern University, Evanston,IL 60208, USA
36
NSF Astronomy and Astrophysics Postdoctoral Fellow
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
Universit`a ‘La Sapienza’, I-00185 Roma, Italy
42
INFN, Sezione di Roma Tre and Universit`a di Roma Tre, Dipartimento diFisica, I-00146 Roma, Italy
43
Universit`a degli Studi di Firenze, I-50121, Firenze, Italy
44
Departament de Fisica, Universitat de les Illes Balears, Cra. ValldemossaKm. 7.5, E-07122 Palma de Mallorca, Spain
45
Nikhef, Science Park 105, 1098 XG Amsterdam, The Netherlands
46
Institut de Ci`encies de l’Espai (CSIC-IEEC), Campus UAB, Torre C-5,parells, 2
na
planta, ES-08193, Bellaterra, Barcelona, Spain
Abstract.
Advanced gravitational wave detectors, currently under construc-tion, are expected to directly observe gravitational wave signals of astrophysicalsrcin. The Einstein Telescope, a third-generation gravitational wave detector,has been proposed in order to fully open up the emerging ﬁeld of gravitationalwave astronomy. In this article we describe sensitivity models for the Einstein
Sensitivity Studies for Third-Generation Gravitational Wave Observatories
3
Telescope and investigate potential limits imposed by fundamental noise sources.A special focus is set on evaluating the frequency band below 10Hz where a com-plex mixture of seismic, gravity gradient, suspension thermal and radiation pres-sure noise dominates. We develop the most accurate sensitivity model, referredto as ET-D, for a third-generation detector so far, including the most relevantfundamental noise contributions.PACS numbers: 04.80.Nn, 95.75.Kk
1. Introduction
The currently operating Gravitational Wave (GW) detectors LIGO [1], Virgo [2],
GEO600 [3] and TAMA [4] are based on extremely sensitive Michelson interferometers.
While the sensitivity achieved by these ﬁrst generation detectors is mainly limitedby shot noise, mirror thermal noise and seismic noise, for the second generationof 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 towards thelow-frequency end of the detection band: Thermal noise of the test mass suspension,photon radiation pressure noise and seismically driven gravity gradients acting onthe test masses. These three sources of noise will become even more important forthird-generation GW observatories such as the Einstein Telescope (ET) [9], [10], as
these detectors aim to signiﬁcantly increase the detection band towards frequenciesas low as a few Hz [11], [13]. Therefore, major parts of the ET design are driven by
exactly these noise sources. An overview of the importance of the sub-10Hz band forastrophysical and cosmological analyses can be found in [9].In this article we will give an overview of the currently ongoing ET designactivities with a special focus on the modelling of the achievable sensitivity takingthe most important fundamental noise sources into account. The ﬁrst sensitivityestimate for a third-generation interferometer was described in [11], [12] and was
based on a single interferometer covering the full frequency range from about 1Hz to10kHz. In the following we will refer to this sensitivity curve as
ET-B
. Subsequentlywe developed a more realistic design, taking cross-compatibility aspects of the variousinvolved technologies into account. This led to the so-called xylophone-design, inwhich 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 willserve as a starting point for the investigations described in this article. We improvedthe sensitivity models for ET by including additional new noise sources as well asby amending and updating noise contributions already previously included. Theseimprovements, which led to a new sensitivity estimate, referred to as
ET-D
, will bepresented and discussed in this article.In section 2 we discuss seismic and gravity gradient noise, followed by the quantumnoise contribution in section 3. Thermal noise of the suspensions and test masses willbe presented in section 4. An improved noise budget for the Einstein Telescope isthen given in section 5. We conclude with a brief overview of the conﬁguration of afull third-generation observatory, consisting of several GW detectors.
Sensitivity Studies for Third-Generation Gravitational Wave Observatories
4
10
−1
10
0
10
1
10
−12
10
−11
10
−10
10
−9
10
−8
10
−7
10
−6
Frequency [Hz]
S e i s m i c d i s p l a c e m e n t [ m / s q r t ( H z ) ]
Black Forest (BFO),12.9.201010
−1
10
0
10
1
10
−20
10
−15
10
−10
10
−5
10
0
Frequency [Hz]
T r a n f e r f u n c t i o n
Superattenuator,17m, 6 stages10
0
10
1
10
−25
10
−24
10
−23
10
−22
10
−21
Frequency [Hz]
S t r a i n [ 1 / s q r t ( H z ) ]
ET−B total noiseET−C total noiseSeismic noise(50m suspension)Seismic noise(17m suspension +Blackforest seismic)
Figure 1.
Seismic noise spectrum from an underground location in the BlackForest, Germany (left hand panel). Transfer function of a superattenuatorconsisting of 6 stages with an overall height of 17m (center panel). The right handpanel shows the resulting seismic noise contribution for the 17m superattenuatorfor the seismic excitation at the Black Forest site (green dashed line). Forcomparison also ET-B and ET-C are plotted. Their seismic noise contribution isbased on the assumption of a generic 5-stage 50m suspension.
2. Seismic Isolation and Gravity Gradient Noise
Seismic noise couples into the diﬀerential arm length of a GW detector via two mainpaths. First of all, seismic excitation can mechanically couple through the suspensionand seismic isolation systems. Secondly, seismic noise excites density ﬂuctuations inthe environment of the GW detector, which couple via gravitational attraction to thetest 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 thesetwo noise sources is that while seismic noise can be reduced by application of complexseismic isolation systems, the only guaranteed way to reduce the gravity gradient noiseis to reduce the initial seismic excitation.
‡
Therefore, third-generation GW detectorsare proposed to be built in quiet underground locations.The seismic noise contribution of the low-frequency interferometer of ET-C wasbased on a seismic excitation of 5
·
10
−
9
m
/
√
Hz
/f
2
(where
f
is the frequency in Hz) anda generic 50m tall seismic isolation system consisting of 5 passive pendulum stages,each of 10m 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 super attenuator willbe extended to 2m per stage. The overall isolation of the proposed modiﬁed superattenuator, consisting of 6 pendulum stages (each stage providing horizontal as wellas vertical isolation) and a total height of 17m, is shown in the center panel of Figure1. Using the seismic excitation level, measured in an underground facility of the BlackForest 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 inthe right hand panel of Figure 1. Reducing the height of the seismic isolation system
‡
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 inthis article.
Sensitivity Studies for Third-Generation Gravitational Wave Observatories
5
10
0
10
1
10
−25
10
−24
10
−23
10
−22
10
−21
Frequency [Hz]
S t r a i n [ 1 / s q r t ( H z ) ]
ET−B total noiseET−C total noiseGravity Gradients
β
=1.2Gravity Gradients
β
=0.6Gravity Gradients
β
=0.3Gravity Gradients
β
=0.15
10
0
10
1
10
2
10
−27
10
−26
10
−25
10
−24
10
−23
10
−22
10
−21
Frequency [Hz]
S t r a i n [ 1 / s q r t ( H z ) ]
ET−C total noise
Suspension thermal noise
Figure 2.
Left panel: Gravity gradient noise contribution to ET, for various
β
values, assuming the BFO spectrum shown in Figure 1 as seismic excitation level.Right panel: Suspension thermal noise of the low frequency interferometer of ETas described in [34]
from 50 to 17m increases the cut-oﬀ frequency only slightly from about 1.2 to 1.7Hz.Gravity gradient noise has been described in detail [20, 21, 22]. In our simulationswe 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
2seis
,
(1)where
G
is the gravitational constant,
ρ
r
the density of the rock around the GWdetector,
L
the arm length of the interferometer,
f
the frequency and
X
2seis
the powerspectral density of the ground motion.
β
accounts for the actual coupling transferfunction from seismic excitation to the diﬀerential arm length noise and depends forinstance on the wave type of the seismic excitation (e.g. ratio of P and S waves) andsoil characteristics.Within the ET design study we carried out a campaign of measuring the seismicnoise in various underground locations across Europe. These measurements haveindicated that a couple of the test locations show a seismic excitation level similar to orbelow the BFO measurement [23]. Therefore, we assumed the BFO seismic excitationas a conservative estimate of a potential ET site. The left panel of Figure 2 showsthe corresponding gravity gradient noise contribution at the BFO site for diﬀerent
β
. Since the detailed evaluation of a realistic
β
for potential ET sites is an ongoingactivity, we will use
β
= 0
.
58, as given in the literature [20, 21], in the following for
the ET-D sensitivity. Please note that our models do not take atmospheric newtoniannoise into account.
3. Shaping of Quantum Noise
Quantum noise, composed of photon shot noise at high-frequencies and photonradiation pressure noise at low frequencies, contributes signiﬁcantly to the overallsensitivity of ET’s high frequency and low-frequency detectors. The high-frequencyinterferometers will feature a light power stored in the arm cavities of about 3MW toreduce shot noise, while the low-frequency interferometers make use of only 18kW of light power in the arms, in order to reduce the radiation pressure noise. For ET-C the

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