The LISA concept

TheLISAconceptKOHEIYAMAMOTOD1INKAJITA LAB

4/22/19 CHUKANHOUKKOKUINANDOLAB 1

4/22/19 CHUKAN HOUKKOKU INANDOLAB 2

2013/4– 2017/3:Facultyofengineering,KyotoUniversityBachelor’sThesis:EvolutionofStressTensorofElectronandNucleibasedonthePrimaryRiggedQED

2017/4– 2019/3:DepartmentofPhysics,theUniversityofTokyo(Kajita lab)Master’sThesis:LasermodulationsystemforinterferometersensingandcontrolforDetunedRSEinKAGRA

2019/4– 2019/6(7?):DepartmentofPhysics,theUniversityofTokyo(Kajita lab)ThankstoIzumi-san,nowstayinginISAS/JAXAinSagamiharaasavisitor

2019/6- :DepartmentofPhysics,LeibnizUniversityHannoverMaxPlanckInstituteforGravitationalPhysics,Hannover(GerhardHeinzel Lab)

SupposedtobelongtotheLISAexperimentalgroup(Specifically,OpticalBenchsubgroup)

Who am I ?

Name:Kohei Yamamoto


Thank you for inviting me today!

Takano,“PleasetellushowyougotadmissionfromAEI”

Enomoto-san,“TellushowLISAdetectsGWs!!!”

HereistworequestsIreceivedwheninvited.


Until I got a new position

Sep Oct Nov Dec Jan Feb Mar2018 2019

SentthefirstemailtoProf.GerhardHeinzel

SkypeConversation:Theyhavealmost10people

Goodopportunitytoletthemknowme

keepintouchonemail

TakeTOEFL👎

Completeapplications• CV• Letters• GPA• Essay

nervouswaitingperiod

• InterviewbyZoom• Gotadmissionon

nextday👍

AEIsetsnodeadlineofapplications


Thank you for inviting me today!

Takano,“PleasetellushowyougotadmissionfromAEI”

Enomoto-san,“TellushowLISAdetectsGWs!!!”

HereistworequestsIreceivedwheninvited.


Today’s talk

• Now,IstudyLISAwithIzumi-sanbasedonthedocument,called“YellowBook”.

• Today’stalkbasicallyfocusesonthegenericpartofLISA,likethesciencetarget,experimentalconcept,anticipatednoisesandwhatever..

※ Somepartsofthecontentsinthisslidemightbeoutoffashionnow…


Contents

ØTheLISAconcept

ØScienceRequirementsOverview• ScienceObjectives• InstrumentalNoisemodelandNoiseallocation

Ø TowardsthedetectionofGW• Time-DelayInterferometry• Payload


The LISA concept

Firstofall,anyway,IlistthreekeyconceptsofLISA.(I’llexplainthepayloadofLISAmoreindetaillater)

• Breakupthemeasurementtothreeparts• Drag-freeoperation

o SurroundthetestmassbyS/CandcontroltherelativepositionofTMandS/Co Topreventthetestmassfromthetime-varyingdisturbance

• Continuouslaserrangingscheme,called“transponder”modeo OneS/Creturnsthehighpowerbeamwhichisphase-lockedtothereceived

beam.


The LISA concept/Break up the measurment to 3 parts

• Whatwewanttomeasure,thepathlengthb/wtestmasses,issplitinto3o One:S/CtoS/Co Two:TestMasstoS/C

• Thisisnecessaryforthetotalphasemeasurementfrommasstomass.

Explainthedetaillater…


Contents

ØTheLISAconcept




From Science Objectives to Instrumental Noise Model (ISM)

ScienceObjectives

・・・

ScienceInvestigation

・・・

ObservationRequirements

・・・

mission’s Purpose Research Quantity(Precision)

ISM

Meetalltherequirements

Here,IshowhowtosettheinstrumentalnoisemodelofLISA.Inthispart,I’llbrieflyexplaineachintheschematic,especiallyscienceobjectivesandISM.


Science Objectives

Here,IlistupthescienceobjectivesinLISAband

• TestofGeneralRelativityMBHsmergerandEMRI

• DeterminethehistoryofBHstogeneratetheMBHsingalacticnucleitodaymapthemassofBHswithredshift

• Surveythousandsofnewcompactstellar-massbinariesFormationhistoryofthemandStructureofGalaxy

• PrecisionCosmology• Newphysics

Cosmologicalbackground,Cosmicstringandunforeseensources


Science Objectives/Test of General Relativity

Sofar,wefoundnoevidenceoftheviolationofGR• Testinsolarsystem• Binarypulsars

Periodderivative• GWsdetectedwiththeground-baseddetector

LISAtestsGRinthemuchstrongergravitationalfieldwiththeSNRashighasseveralthousands.Therearetwosourcesgoodforthispurposeo MergerofMBHso ExtremeMassRatioInspirals (EMRI)


• 。※Roughlycomparablemass

• Inspiral: Thelast10# − 10% cyclesininspiral phasecanbedetectedo Massandspinscanbedeterminedtohighaccuracyo Leadstogoodpredictionoftheburstwaveform

• Merger: ThepredictedwaveformbasedonGRcanbecomparedtotheobservedburstsignals.->IdealtestofGRAmplitudeoftheburstwaveformissolargethatitisvisiblebyeyeinthedatastream(seeFig.1).

• Ringdown:WecanderivethemassandspinofeachBHfromtheringdown parameter:FrequencyandDampingtime.

Fig.1

Fig.2(“L3missionconcepts”)

Science Objectives/Test of General Relativity/MBHs


Science Objectives/Test of General Relativity/EMRI

Trapped!

• Massratio:10&# − 10&'

• Non-zeroeccentricity

• DurationtimenearISCO:fewdecades->ForLISA’sentireobservationtime,theorbitsarehighlyrelativistic

• Afitofthewaveformisverysensitive->Computationallycost,butextremelyaccuratedeterminationofparameters,i.e.determinemassandspintoaccuracyof10&% − 10&(

Thisleadstothepreciseobservationaltestofthe“Kerr-ness”ofthecentralMBH.

GenericEMRIwaveforms


Science Investigation and Observation RequirementHereisthescienceinvestigationsandobservationrequirementsof“TestofGR”

ScienceInvestigations ObservationRequirement

SI:researchneededtofulfillscientificobjectivesOR:observablequantitiesnecessaryfortheSIandtheprecisionwithwhichtheymustbemeasured


Contents

ØTheLISAconcept




Instrument Sensitivity Model (ISM)

ISM:Thenoisepermittedsothatthesensitivityfulfillthesciencerequirements※Thiscombinesaninstrumentalnoisemodewiththeantenna’stransferfunctions

Averageoverthefullsky = 𝟏/𝐬𝐢𝐧(𝟔𝟎°):

Projectioneffect

Antenna’sTFNoisemodel(budget=requirement)• IMS:Displacementnoisefrom

themeasuringsystem• DRS:Displacementnoisefrom

SpuriousaccelerationsonTM


ISM/Antenna’s TFThisiswhatweusuallycallthefrequencyresponseofthedetectortoGWs

※Thisisforthebaselineof𝟓×𝟏𝟎𝟗mFortheapproximationofT(f),thefollowingequationcanbeused,

𝑓8:ThefrequencyatwhichthecancellationoftheGWsignalstarts,= 9

:;= 30mHz

a: 0.41Cornerfrequencyshouldincreasebyafactorof2


ISM/Noise model

Ø 𝛿𝑥?@A(𝑓): accelerationnoise,convertedtodisplacement,oftheDisturbanceReductionSystem(DRS)

Ø 𝛿𝑥BCA(𝑓):displacementnoisefromtheInterferometricMeasuringSystem(IMS)

Δ𝑎8 = 3, 𝑓G = 8mHz,𝑓; = 0.1mHz

Dominantatlowfrequency

Dominantathighfrequency

Δ𝑥8 = 18, 𝑓G = 2.8mHz


Instrument Sensitivity Model (ISM)

HereisthedisplacementnoiseamplitudespectraldensityfromtheISM.

Weneedtoforeseetheamountofnoiseofacertainsubsystem.Thisiscalledallocation


Noise allocation

Inamplitudespectraldensity,theallocationis65%ofthebudget,i.e.requirement.Thismarginisforcontingencyinscienceperformance.

Dominant


LISA band

Ref:C.J.Mooreetal,“Gravitational-wavesensitivitycurves”,ClassicalandQuantumGravity


Contents

ØTheLISAconcept


Ø TowardsthedetectionofGW• Phasemeasurement• Frequencystabilization


𝑳𝟏

𝑳𝟐

• Thebasicconceptis“Michelsoninterferometer”ofthetwopath※ Thirdlinkscontributestotheimprovementbyafactorof 2�

• IfweconfigurethestandardMI,thefrequencynoiseistoolargetodetecttheGWbecause𝚫𝑳 = |𝑳𝟏 − 𝑳𝟐| canbeupto𝟏𝟎𝟖m

• LISAmeasures𝐿R and𝐿: independentlyandcombinesthedataseriesinpostprocessing,calledTime-delayInterferometry

Towards the detection of GWs


HowdoesLISAmeasurethepathlength? HowdoesLISAstabilizethelaserfrequency?

• MassInterferometer

• ScienceInterferometer

• Pre-stabilization

• Armlocking(Transponder)

• Time-DelayInterferometry

Two main topics here

Nowweconfronttwoquestions


Phase measurement

Canwedirectlymeasurethedistancefromtestmasstotestmass?

𝑳

𝒍𝟏

𝝋𝒔𝒊𝒈 = 𝟐𝝋𝑳 + 𝝋𝒍𝟏

Withonlyonephasemeasurement,it’sdifficulttoextractthe𝟐𝝋𝑳 fromthemeasuredphasedifference,𝝋𝒔𝒊𝒈.

Thephasemeasurementisbrokenupto3parts


Phase measurement/3parts • Conceptually,onewaypathisenoughforthemeasurementof𝐿 = 𝐿Y + 𝑙R + 𝑙:

• ScienceInterferometer:measure𝜑;Y• MassInterferometer:measure𝜑\R (and𝜑\: onOB2)

OB1 OB2

𝑳′𝒍𝟏 𝒍𝟐

Topview

However,theGWsignalisobviouslyunderthefrequencynoiselevel𝛿𝜈_`abb = 3MHz/rtHz,while𝛿𝜈_abc = 1.2×10&dHz/rtHz

To/FromTestMass

FromOB2


Frequency Stabilization

Hereisthenoiserequirementoffrequencystabilization

• Thereductionoffrequencynoisebyabout12ordersofmagnitudeisneeded

• Pre-stabilization:thebasicschemewiththereferencecavity

• Armlocking:PLLbetweenS/Cs(transponder)• TDI:Linearcombinationofdataseriesinpost

processing


Frequency Stabilization/Pre-stabilization

ReferenceCavity

SG

PhaseShifter

PBS QWP

RFPD

• Theusualschemewithareferencecavityisimplemented

• OneofthelaserinS/CisstabilizedbythisPDHtechnique

• TheotherinthesameS/Cisphase-lockedtothisstabilizedlaserbyso-called,referenceinterferometer


Frequency Stabilization/Pre-stabilization

MassInterferometer:𝜑efgg

ReferenceInterferometer:𝜑ab`

• Referenceinterferometerisusedforthephase-lockingb/wtheprimarylaserandsecondaryone

• Byusingthesecondarylaseralsoforthemassinterferometer,wecanfurtherreducethephase(frequency)noise.o 𝜑ab`(𝑡) = 𝜑R(𝑡) − 𝜑:(𝑡) + 𝑛`(𝑡)o 𝜑efgg 𝑡 = 𝜑R 𝑡 − 𝜑: 𝑡 + 𝑘Δ𝐿efgg + 𝑛`(𝑡)

𝜑R,::Phaseofprimaryandsecondarylaser𝑛`:noiseinback-linkfiberΔ𝐿efgg:relativepositionoftestmassagainstOB


Frequency Stabilization/Arm locking(transponder)

• Intranspondermode,thetransmittedbeamisphase-lockedtothereceivedbeam

• Thisisforgeneratingthehighpowerreplica

• Atthesametime,thisactasthesecondfrequencystabilization

Ref:Yian Yu,doctral thesis,UF


Frequency Stabilization/Arm locking(transponder)

+-

𝐺l

+-

+

𝜑m

𝜑l

+

𝐺m

+

ScienceInterferometerA

BScienceInterferometer

+

𝜑;

Wecanseehowthefrequencynoiseiscancelledbythephase-lockingb/wtransmittedandreceivedlaser

−𝐺l𝐵 + 𝜑l − 𝜑; − 𝐺m𝐴 + 𝜑m = 𝐵−𝐺m𝐴 + 𝜑m − 𝜑; − 𝐺l𝐵 + 𝜑l = 𝐴

(1)(2)

From(1)and(2),thesignalofthescienceinterferometerisderived:

𝐴 = −1 + 2𝐺l1 + 𝐺 𝜑; +

𝜑m1 + 𝐺 −

𝜑l1 + 𝐺

𝐵 = −1 + 2𝐺m1 + 𝐺 𝜑; +

𝜑l1 + 𝐺 −

𝜑m1 + 𝐺

(3)

(4)

0𝜑;

When𝐺m, 𝐺l ≫ 1BlockDiagramofthetranspondermode

Withoutthephase-locking,thesignalishighlyaffectedbyfrequencynoise𝐴 = 𝜑m − 𝜑l + 𝜑;


Frequency Stabilization • Onlyonemasterlaserhasthecavitytobepre-stabilized.

• Otherlasersarestabilizedbythereferenceinterferometerorarmlocking

• Thisleadstothefrequencynoisewiththesameorderastheground-baseddetector

• Butthelargedifferenceinthepathlengthpreventtheresidualnoisefrombeingcancelled

• LISAutilizethetechnique,calledTDI,duringpost-processing tosolvethisproblem


Frequency Stabilization/TDIAssumption:

1. LasersintheoneS/C1canbeconsideredas“identical”ones->BSinthestandardMI2. S/C2&3canbeconsideredas“mirrors”becauseoftransponder3. Armlengthisfixed

1

2 3

𝝋𝒔𝒄𝒊𝟑𝝋𝒔𝒄𝒊𝟐

Withtheseassumptions,thesignalofthescienceinterferometercanbederivedlikethefollowing.

𝜑g9t: 𝑡 = 𝜑R 𝑡 − 𝜑R 𝑡 −2𝐿:𝑐 + ℎ: 𝑡

𝜑g9t( 𝑡 = 𝜑R 𝑡 − 𝜑R 𝑡 −2𝐿(𝑐 + ℎ( 𝑡

𝑳𝟐𝑳𝟑

(1)

(2)

Fromthesedataseries,wecancalculatethelinearcombinationsuchthatthephasenoiseiscancelled.

𝑋 ≡ 𝜑g9t: 𝑡 − 𝜑g9t( 𝑡 − 𝜑g9t: 𝑡 −2𝐿(𝑐 +𝜑g9t( 𝑡 −

2𝐿:𝑐

= ℎ: 𝑡 − ℎ( 𝑡 − ℎ: 𝑡 −2𝐿(𝑐 + ℎ( 𝑡 −

2𝐿:𝑐

ThisiscalledMichelsonX-combination


Ref:Tinto“Time-DelayInterferometry”

𝐿: 𝐿(

Frequency Stabilization/TDIThiscombinationcanbeinterpretedasthereconstructionoftheequal-armedMichelsoninterferometerandcancelthecommonphasenoiselikeastandardMIdoes.

𝑋 = [𝜑g9t: 𝑡 +𝜑g9t( 𝑡 −2𝐿:𝑐 ] − [𝜑g9t( 𝑡 + 𝜑g9t: 𝑡 −

2𝐿(𝑐 ]

Thesetwotermsareconsideredaslaserswhichhavepropagatesinthesamedistance,𝐿: + 𝐿(,andarecombinedattimeoftatS/C1.

Wecannaturallyunderstandthiscombinationcancelthephasenoise


Frequency Stabilization/TDI

• TDItechniquehasbeendemonstratedbytheLISAinterferometrytestbed

• Thelaserphasenoiseissuppressedby9orderofmagnitudedowntotheinterferometerlimitandLISArequireement.


Topics of my research @ AEI

TTLishere

• OneexampleistheresearchoftheTilt-to-Length(TTL)coupling,whichhasgreatcontributionstothedisplacementnoiseandoftenlimitthesensitivity

• Anotheristhetestofphasemeterwithanuniqueinterferometer,calledHexagon• MaintargetofmyresearchcanbetheestimationofthedisplacementnoisewithlinksanddeveloptheLISA

interferometrychainfurthersothatitmeetstherequirement.


Appendix

The LISA concept

Documents

Transcript of The LISA concept