NASA Technical Reports Server (NTRS) 20120013339: Doing Science with eLISA: Astrophysics and Cosmology in the Millihertz Regime

1.3 MB·English

by  NASA Technical Reports Server (NTRS)

Doing science with eLISA:
Astrophysics and cosmology in the millihertz regime
PauAmaro-Seoane1,13,SofianeAoudia1,StanislavBabak1,PierreBinétruy2,EmanueleBerti3,4,
AlejandroBohé5,ChiaraCaprini6,MonicaColpi7,NeilJ.Cornish8,KarstenDanzmann1,
2
1Jean-FrançoisDufaux2,JonathanGair9,OliverJennrich10,PhilippeJetzer11,AntoineKlein11,8,Ryan
0 N.Lang12,AlbertoLobo13,TysonLittenberg14,15,SeanT.McWilliams16,GijsNelemans17,18,19,
2AntoinePetiteau2,1,EdwardK.Porter2,BernardF.Schutz1,AlbertoSesana1,RobinStebbins20,Tim

n Sumner21,MicheleVallisneri22,StefanoVitale23,MartaVolonteri24,25,andHenryWard26
a
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o 1MaxPlanckInstitutfürGravitationsphysik(Albert-Einstein-Institut),Germany
r 2APC,Univ.ParisDiderot,CNRS/IN2P3,CEA/Irfu,Obs.deParis,SorbonneParisCité,France
st 3DepartmentofPhysicsandAstronomy,TheUniversityofMississippi,University,MS38677,USA
a 4DivisionofPhysics,Mathematics,andAstronomy,CaliforniaInstituteofTechnology,PasadenaCA91125,USA
[ 5UPMC-CNRS,UMR7095,Institutd’AstrophysiquedeParis,F-75014,Paris,France
6InstitutdePhysiqueThéorique,CEA,IPhT,CNRS,URA2306,F-91191Gif/YvetteCedex,France
1 7UniversityofMilanoBicocca,Milano,I-20100,Italy
v 8DepartmentofPhysics,MontanaStateUniversity,Bozeman,MT59717,USA
1 9InstituteofAstronomy,UniversityofCambridge,MadingleyRoad,Cambridge,CB30HA,UK
2 10ESA,Keplerlaan1,2200AGNoordwijk,TheNetherlands
6 11InstituteofTheoreticalPhysicsUniversityofZürich,Winterthurerstr.190,8057ZürichSwitzerland
3 12WashingtonUniversityinSt.Louis,OneBrookingsDrive,St.Louis,MO63130,USA
. 13InstitutdeCiènciesdel’Espai(CSIC-IEEC),CampusUAB,TorreC-5,parells,2naplanta,ES-08193,Bellaterra,Barcelona,Spain
1 14MarylandCenterforFundamentalPhysics,DepartmentofPhysics,UniversityofMaryland,CollegePark,MD20742
0 15GravitationalAstrophysicsLaboratory,NASAGoddardSpaceflightCenter,8800GreenbeltRd.,Greenbelt,MD20771,USA
2 16DepartmentofPhysics,PrincetonUniversity,Princeton,NJ08544,USA
1 17DepartmentofAstrophysics,RadboudUniversityNijmegen,TheNetherlands
: 18InstituteforAstronomy,KULeuven,Celestijnenlaan200D,3001Leuven,Belgium
v
19Nikhef,SciencePark105,1098XGAmsterdam,TheNetherlands
i
X 20NASALiason,NASAGSFC,USA
21ImperialCollege,UK
ar 22JetPropulsionLaboratory,CaliforniaInst.ofTechnology,Pasadena,CA91109,USA
23UniversityofTrento,DepartmentofPhysics,I38050Povo,Trento,Italy
24Institutd’AstrophysiquedeParis,98bisBoulevardArago,75014Paris,France
25AstronomyDepartment,UniversityofMichigan,AnnArbor,MI48109,USA
26InstituteforGravitationalResearch,DepartmentofPhysics&AstronomyKelvinBuilding,UniversityofGlasgow,Glasgow
eLISA:Astrophysicsandcosmologyinthemillihertzregime
Contents
1 Introduction 5
2 Descriptionofthemission 6
3 Ultra-CompactBinaries 9
1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Instrumentverification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 eLISAasaworkhorse:thousandsofnewbinaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1 TypeIasupernovaeandsub-luminoussupernovae . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4 StudyingtheastrophysicsofcompactbinariesusingeLISA . . . . . . . . . . . . . . . . . . . . . . . . . 14
5 StudiesofgalacticstructurewitheLISA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 AstrophysicalBlackHoles 20
1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2 Blackholesintherealmoftheobservations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Galaxymergersandblackholecoalescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4 Dual,binaryandrecoilingAGNinthecosmiclandscape . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5 Seedblackholes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6 Evolvingmassiveblackholespinsviacoalescenceandaccretionevents . . . . . . . . . . . . . . . . . . 29
7 Cosmologicalmassiveblackholemergerrate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
8 Massiveblackholebinariesasgravitationalwavessources:whatcaneLISAdiscover? . . . . . . . . . . 32
9 ReconstructingthemassiveblackholecosmichistorythrougheLISAobservations . . . . . . . . . . . . 37
5 Extrememassratioinspiralsandastrophysicsofdensestellarsystems 40
1 TheGalacticCentre:auniquelaboratory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2 ExtremeMassRatioInspiralsingalacticnuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3 Aprobeofgalacticdynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 Aprobeofthemassesofstellarandmassiveblackholes . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5 DetectingextrememassratioinspiralswitheLISA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
6 EstimatingtheeventratesofextrememassratioinspiralsforeLISA . . . . . . . . . . . . . . . . . . . . 45
7 Blackholecoalescenceeventsinstarclusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6 ConfrontingGeneralRelativitywithPrecisionMeasurements
ofStrongGravity 46
1 Settingthestage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
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2 Testingstrong-fieldgravity:Theinspiral,merger,andringdownofmassiveblackholebinaries . . . . . . 48
3 Extrememassratioinspirals:precisionprobesofKerrspacetime . . . . . . . . . . . . . . . . . . . . . . 50
4 Intermediatemassratiobinaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5 Themassofthegraviton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
7 Cosmology 54
1 NewphysicsandtheearlyUniverse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2 CosmologicalmeasurementswitheLISA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
8 Conclusions:scienceandobservationalrequirements 60
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Abstract
ThisdocumentintroducestheexcitingandfundamentallynewscienceandastronomythattheEuropeanNewGravitational
WaveObservatory(NGO)mission(derivedfromthepreviousLISAproposal)willdeliver. Themission(whichwewill
refer to by its informal name “eLISA”) will survey for the first time the low-frequency gravitational wave band (about
0.1 mHz to 1 Hz), with sufficient sensitivity to detect interesting individual astrophysical sources out to z = 15. The
measurementsdescribedherewilladdressthebasicscientificgoalsthathavebeencapturedinESA’s“NewGravitational
Wave Observatory Science Requirements Document”; they are presented here so that the wider scientific community
can have access to them. The eLISA mission will discover and study a variety of cosmic events and systems with
high sensitivity: coalescences of massive black holes binaries, brought together by galaxy mergers; mergers of earlier,
less-massive black holes during the epoch of hierarchical galaxy and black-hole growth; stellar-mass black holes and
compactstarsinorbitsjustskimmingthehorizonsofmassiveblackholesingalacticnucleiofthepresentera;extremely
compactwhitedwarfbinariesinourGalaxy,arichsourceofinformationaboutbinaryevolutionandaboutfutureType
Iasupernovae;andpossiblymostinterestingofall,theuncertainandunpredictedsources,forexamplerelicsofinflation
andofthesymmetry-breakingepochdirectlyaftertheBigBang. eLISA’smeasurementswillallowdetailedstudiesof
these signals with high signal-to-noise ratio, addressing most of the key scientific questions raised by ESA’s Cosmic
Visionprogrammeintheareasofastrophysicsandcosmology. Theywillalsoprovidestringenttestsofgeneralrelativity
inthestrong-fielddynamicalregime, whichcannotbeprobedinanyotherway. Thisdocumentnotonlydescribesthe
sciencebutalsogivesanoverviewonthemissiondesignandorbits. LISA’sheritageintheeLISAdesignwillbeclearto
thosefamiliarwiththepreviousproposal,aswillitsincorporationofkeyelementsofhardwarefromtheLISAPathfinder
mission, scheduled for launch by ESA in 2014. But eLISA is fundamentally a new mission, one that will pioneer the
completelynewscienceoflow-frequencygravitationalwaveastronomy.
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1 Introduction
OurviewoftheUniversehaschangeddramaticallyoverthepastcentury.LessthanahundredyearsagoourownGalaxy,
theMilkyWay,wasbelievedtobeourownisland-Universe. Thediscoveryofhundredsofbilliongalaxieslikeourown,
andofbillionluminoussourcessuchasQuasiStellarObjects(QSOs),changedourperceptionofthecosmiclandscape.
NewastronomicalobjectswerediscoveredwiththeadventofradioandX-rayAstronomy.Relativisticbinariescomposed
ofcompactstars(suchaswhitedwarfsorneutronstars)andstellar-massblackholesareamongthesesourcesofelectro-
magneticradiation. Accordingtotheaccretionparadigm, supermassiveblackholesatgalacticcentresarethesimplest
explanationforthepoweremittedbydistant,luminousQSOs,butaconclusivetestofthishypothesisisstilllacking.
The remarkable discovery of the recession of galaxies and of the fossil microwave background radiation, almost
contemporarytothediscoveryofX-raysources, hasfurtherledtotheemergenceofacosmologicalparadigm, theBig
Bang,thathasrevolutionizedourdescriptionoftheUniverse. WenowknowthatourUniversehadabeginningandthat
itsluminouscomponents(inparticular,galaxiesandQSOs)evolvejointlyandinconcordancewiththeevolutionofthe
underlyingdarkmatterpermeatingtheUniverse.
AccordingtoGeneralRelativity,blackholesandcompactbinariesareexpectedtobepowerfulsourcesofgravitational
waves. Ratherthan“seeing”electromagneticradiation,asallofastronomyhasdoneuntilpresent,eLISAwill“hear”the
vibrationsofthefabricofspacetimeitself,emittedcoherentlybymacroscopicbodies.Studyingthesesignalswillconvey
richnewinformationaboutthebehaviour,thestructureandthehistoryoftheUniverse,anditwillclarifyseveralissues
infundamentalphysics.
Gravitationalwavestravelundisturbedthroughspacetime,andwhenobservedtheyofferanewanduniquelypowerful
waytoprobetheverydistantUniverse,fromtheextremelyearlyBigBangtotheearlyepochofgalaxyandblackhole
seedformation. Thismayallowustoaddressdeepquestions. WhatpoweredtheBigBang? Howdidgalaxiesandtheir
blackholesformandevolve?Whatisthestructureofspacetimearoundthemassiveobjectswebelievetobeblackholes?
WhatisthenatureofthemysteriousdarkmatteranddarkenergyacceleratingtheexpansionoftheUniverse?
eLISAisaspace-basedmissiondesignedtomeasuregravitationalradiationoverabroadbandatfrequenciesranging
between f ∼ 0.1 mHz and f ∼ 1 Hz. In this frequency band the Universe is richly populated by strong sources of
gravitationalwaves. Forbinarysystemsthecharacteristicgravitational-wavefrequency f istwicetheKeplerianorbital
frequency,whichinturnisproportionalto(M/a3)1/2,whereMisthetotalmassofthebinaryandaitssemi-majoraxis.In
theeLISAfrequencyband,gravitationalwavesareproducedbyclosebinariesofstellar-massobjectswithorbitalperiods
ofafewtoseveralminutes. MassiveblackholebinarieswithM ∼104M(cid:3)−107M(cid:3)andmassratio0.01(cid:2)q(cid:2)1onthe
vergeofcoalescinghaveorbitalfrequenciessweepingtohigherandhighervalues,untilthebinaryseparationabecomesas
smallasthescaleoftheeventhorizonGM/c2.Finally,eLISAcouldobservebinariescomprisingamassiveblackholeand
astellar-masscompactobject(e.g.,astellar-massblackhole)skimmingthehorizonofthelargerblackholebeforebeing
captured: these systems are commonly referred to as extreme mass ratio inspirals (EMRIs). Furthermore, a stochastic
backgroundintheeLISAfrequencybandcanbegeneratedbylessconventionalsources,suchasphasetransitionsinthe
veryearlyUniverseand/orcosmicstrings.
ThisnoteisacomprehensivesurveyoftheeLISAsciencecase.Weconsideralltherelevantastrophysicalandcosmo-
logicalgravitationalwavesourcesandexploreeLISAdetectionperformancesintermsofsensitivity,SNRdistributions,
andparameterestimation.
InSection2wewillbrieflydescribethemissionconceptandthebasicdesignoftheinstrument,introducingtheeLISA
sensitivitycurvethatwillbeusedthroughoutthestudy.
OursurveyoftheeLISAsciencecasewillstartinSection3byexploringthenearestobservablesourcesofgravitational
waves, i.e. compact stellar-mass binaries in the Milky Way. eLISA will study the gravitational wave signals from
thousands of stellar-mass close binaries in the Galaxy and will give information on the extreme endpoints of stellar
evolution. eLISAwillprovidedistancesanddetailedorbitalandmassparametersforhundredsofthesebinaries. This
isarichtroveofinformationformappingandreconstructingthehistoryofstarsintheGalaxy,anditcanrevealdetails
ofthetidalandnon-gravitationalinfluencesonthebinaryevolutionassociatedwiththeinternalphysicsofthecompact
remnantsthemselves.
Thenwewillsummarizethescienceobjectivesthatarerelevantfortheastrophysicsofblackholes(Section4).Current
electromagneticobservationsareprobingonlythetipoftheblackholemassdistributionintheUniverse,targetingblack
holeswithlargemasses,between107M(cid:3) and109M(cid:3). Conversely,eLISAwillbeabletodetectthegravitationalwaves
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emittedbyblackholebinarieswithtotalmass(inthesourcerestframe)assmallas104M(cid:3) andupto107M(cid:3),outtoa
redshiftaslargeasz∼20. eLISAwilldetectfiducialsourcesouttoredshiftz∼10,andsoitwillexplorealmostallthe
mass-redshiftparameterspacerelevantforaddressingscientificquestionsontheevolutionoftheblackholepopulation.
Redshiftedmasseswillbemeasuredtoanunprecedentedaccuracy,uptothe0.1–1%level,whereasabsoluteerrorsinthe
spindeterminationareexpectedtobeintherange0.01to0.1,allowingustoreconstructthecosmicevolutionofmassive
blackholes.BlackholesareexpectedtotransitintothemassintervaltowhicheLISAissensitivealongthecourseoftheir
cosmicevolution. Thus,eLISAwillmapandmarkthelociwheregalaxiesformandcluster,usingblackholesasclean
tracersoftheirassembly.
eLISAwillalsobringanewrevolutionaryperspectivetothestudyofgalacticnuclei,asshowninSection5. Orbits
ofstellarobjectscapturedbythemassiveblackholeatthegalacticcentreevolvebygravitationalradiation. Bycapturing
theirsignal, eLISAwillofferthedeepestviewofnearbygalacticnuclei, exploringregionsthatareinvisibletoelectro-
magnetictechniques.eLISAwillprobethedynamicsofcompactobjectsinthespace-timeofaKerrblackhole,providing
informationonthespacedensityofthoseobjects.
In Section 6 we address key questions concerning the nature of spacetime and gravity. GR has been extensively
testedintheweakfieldregime,bothinthesolarsystemandviabinarypulsarobservations. eLISAwillprovideaunique
opportunity to probe GR in the strong field limit. eLISA will observe the coalescence of massive black hole binaries
movingatspeedsclosetothespeedoflight,andenableustotestthedynamicsofcurvedspacetimewhengravitational
fieldsarestrong. Byobservingalargenumberoforbitalcyclesduringthelastfewyearsoftheinspiralofastellarmass
objectintoamassiveblackhole,eLISAwillallowustomeasurepreciselytheparametersofthecentralobject(including
its quadrupole moment) in the near Universe. Any deviations in the orbital motion from GR predictions will leave an
imprint in the gravitational wave phase. Thus, measurements of the mass, spin and quadrupole moment of the central
object will allow us to check the Kerr nature of the central massive object, and to test for the first time the black hole
hypothesis.
Lastly,aswedescribeinSection7,eLISAwillprobenewphysicsandcosmologywithgravitationalwaves,andsearch
forunforeseensourcesofgravitationalwaves. TheeLISAfrequencybandintherelativisticearlyUniversecorresponds
to horizon scales where phase transitions or extra dimensions may have caused catastrophic, explosive bubble growth
andefficientgravitationalwaveproduction.eLISAwillbecapableofdetectingastochasticbackgroundfromsuchevents
fromabout100GeVtoabout1000TeV,ifgravitationalwavesintheeLISAbandwereproducedwithsufficientefficiency.
Inclosingthenote, wewillpresentasummaryofthescienceobjectivesoftheeLISAmission. Wesummarizethe
keytheoreticalandobservationalgoalsoftheeLISAsciencecaseinSection8. There,inaschematicbullet-pointform,
weenumeratethescientificgoalsrelatedtoeachclassofgravitationalwavesourcesandtheobservationalperformance
ofeLISAinachievingsuchgoals.ThiscouldserveasacompactsummaryofeLISAscience,aswellasareferencepoint
forotherspace-basedgravitationalwavedetectorproposals.
2 Description of the mission
eLISAisaEuropean-ledvariantofLISAthatcanbelaunchedbefore2022.Thebasicprincipleofgravitationalwavede-
tectionforeLISAisthesameasforLISA:itisalaserinterferometerdesignedtodetectthepassageofagravitationalwave
bymeasuringthetime-varyingchangesofopticalpathlengthbetweenfree-fallingmasses.Manydesignandtechnological
developmentsweremigratedfromLISA,howevertherearesomesubstantialdifferences.
ThetwomeasurementarmsaredefinedbythreespacecraftorbitingtheSuninatriangularconfiguration(seefigure1).
AkeyfeatureoftheeLISAconceptisasetofthreeorbitsthatmaintainanear-equilateraltriangularformationwithan
armlength L = 109m, without the need for station-keeping. Depending on the initial conditions of the spacecraft, the
formationcanbekeptinanalmostconstantdistancetotheEarthorbeallowedtoslowlydriftawaytoabout70×109m,
theouterlimitforcommunicationpurposes.AveryattractivefeatureoftheeLISAorbitsisthealmostconstantsun-angle
of 30 degrees with respect to the normal to the top of the spacecraft, thereby resulting in an extremely stable thermal
environment,minimizingthethermaldisturbancesonthespacecraft.
Oneofthethreespacecraftservesasthe“centralhub”anddefinestheapexofa“V”.Twoother,simplerspacecraft
arepositionedattheendsoftheV-shapedconstellation. Thecentralspacecrafthousestwofree-falling“testmasses”that
definetheendpointofthetwointerferometerarms. Theotherspacecraftcontainonetestmasseach,definingtwomore
endpoints(seefigure2). Eachspacecraftaccommodatestheinterferometryequipmentformeasuringchangesinthearm
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Earth 1 × 109 m
20°
60°
1 AU
Sun
Figure1: TheeLISAorbits: TheconstellationisshowntrailingtheEarthbyabout20degrees(or5×1010km)andis
inclinedby60degreeswithrespecttotheecliptic. Thetrailinganglewillvaryoverthecourseofthemissionduration
from10degreesto25degrees.TheseparationbetweenthespacecraftisL=1×109m.
length. For practical reasons, this measurement is broken up into three distinct parts (see figure 3): the measurement
betweenthespacecrafts,i.e. betweentheopticalbenchesthatarefixedtoeachspacecraft,andthemeasurementbetween
eachofthetestmassesanditsrespectiveopticalbench. Thosemeasurementsarerecombinedinawaythatallowsusto
reconstructthedistancebetween thetestmasseswhichisinsensitive tothenoiseinthepositionof thespacecraftwith
respecttothetestmasses.
AsecondkeyfeatureoftheeLISAconceptisthatthetestmassesareprotectedfromdisturbancesasmuchaspossible
byacarefuldesignandthe"drag-free"operation. Toestablishthedrag-freeoperation, ahousingaroundthetestmass
sensestherelativepositionoftestmassandspacecraft,andacontrolsystemcommandsthespacecraftthrusterstofollow
the free-falling mass. Drag-free operation reduces the time-varying disturbances to the test masses caused by force
gradientsarisinginaspacecraftthatismovingwithrespecttothetestmasses. Therequirementsonthepowerspectral
densityoftheresidualaccelerationofthetestmassis
(cid:2) (cid:3)
10−4Hz
Sx,acc(f)=2.13×10−29 1+ m2s−4Hz−1 (1)
f
or
(cid:2) (cid:3)
10−4Hz Hz
Sx,acc(f)=1.37×10−32 1+ f f4m2Hz−1, (2)
where f isthefrequency.
Thethirdkeyfeature,thedistancemeasuringsystem,isacontinuousinterferometriclaserrangingscheme,similarto
thatusedforradar-trackingofspacecraft.Thedirectreflectionoflaserlight,suchasinanormalMichelsoninterferometer,
isnotfeasibleduetothelargedistancebetweenthespacecrafts. Therefore, lasersattheendsofeacharmoperateina
"transponder" mode. A laser beam is sent out from the central spacecraft to an end spacecraft. The laser in the end
spacecraftisthenphase-lockedtotheincomingbeamthusreturningahigh-powerphasereplica. Thereturnedbeamis
received by the central spacecraft and its phase is in turn compared to the phase of the local laser. A similar scheme
isemployedforthesecondarm. Inaddition,thephasesofthetwolasersservingthetwoarmsarecomparedwithinthe
centralspacecraft.Thecombinedsetofphasemeasurementstogetherwithsomeauxiliarymodulationallowstodetermine
therelativeopticalpathchangeswithsimultaneoussuppressionofthelaserfrequencynoiseandclocknoisebelowthe
secondary (acceleration and displacement) noise. The displacement noise has two components: the shot noise, with a
requiredpowerspectraldensity
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locallasercomparison
PLL
endspacecraft1
sciencemeasurement
Laser
Testmasses
cornerspacecraft endspacecraft2
Figure 2: The constellation of the three eLISA spacecraft constitutes the science instrument. The central spacecraft
harborstwosend/receivelaserrangingterminals,whiletheendspacecrafthasoneeach. Thelaserintheendspacecraft
isphase-lockedtotheincominglaserlight. Thebluedotsindicatewhereinterferometricmeasurementsaretaken. The
sketchleavesoutthetestmassinterferometersforclarity.
MeasurementS/Ctotestmass MeasurementS/Ctotestmass
S/CtoS/Cmeasurement
Figure 3: Partition of the eLISA measurement. Each measurement between two test masses is broken up into three
different measurements: two between the respective test mass and the spacecraft and one between the two spacecraft
(S/C).AsthenoiseinthemeasurementisdominatedbytheshotnoiseintheS/C-S/Cmeasurement,thenoisepenaltyfor
thepartitioningofthemeasurementisnegligible. Theblue(solid)dotsindicatewheretheinterferometricmeasurements
aretaken.
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1e-17
Simulation of LISA
Simulation of ELISA
1e-18 Analytical approximation
)
2 1e-19
1/
-z
H
( 1e-20
y
t
i
v
i
it 1e-21
s
n
e
s
n
i 1e-22
a
r
t
s
1e-23
1e-24
1e-05 0.0001 0.001 0.01 0.1 1
Frequency (Hz)
Figure4: SensitivityofeLISA(averagedoverallskylocationsandpolarisations)versusfrequency: thesolidredcurve
isobtainednumericallyusingthesimulatorLISACode2.0(Petiteauetal.,2008)andthedashedbluecurveistheanalytic
approximationbasedonequation5.Forareference,wealsodepictthesensitivitycurveofLISA(dotted,greencurve).
Sx,sn(f)=5.25×10−23 m2Hz−1 (3)
andtheother(combined)measurementnoisewitharequiredpowerspectraldensity
Sx,omn(f)=6.28×10−23 m2Hz−1. (4)
According to the requirements, eLISA achieves the strain noise amplitude spe(cid:5)ctral density (often called sensitivity)
showedinfigure4whichcanbeanalyticallyapproximateash˜(f)=2δ(cid:4)L(f)/L= S(f),where:
⎛ ⎛ ⎞ ⎞
S(f)= 20 4Sx,acc(f)+Sx,sn(f)+Sx,omn(f)⎜⎜⎜⎜⎜⎜⎜⎝1+⎜⎜⎜⎜⎜⎜⎝ f(cid:9) (cid:10)⎟⎟⎟⎟⎟⎟⎠2⎟⎟⎟⎟⎟⎟⎟⎠ , (5)
3 L2 0.41 c
2L
Thisallowstode√tectastrainofabout3.7×10−24 ina2-yearmeasurementwithanSNRof1(displacementsensitivity
of 11×10−12m/ Hz over a path length of 1×109m). The feasible reduction of disturbances on test masses and the
displacementsensitivitiesachievablebythelaserrangingsystemyieldausefulmeasurementfrequencybandwidthfrom
3×10−5Hzto1Hz(therequirementis10−4Hzto1Hz;thegoalis3×10−5Hzto1Hz).
3 Ultra-Compact Binaries
1 Overview
The most numerous sources in the low-frequency gravitational wave band are ultra-compact binary stars: double stars
in which two compact objects, such as white dwarfs and neutron stars, orbit each other with short periods. They have
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Figure5: Artistimpressionofadetacheddoublewhitedwarfbinary(left)andaninteractingbinaryinwhichaneutron
staraccretesmaterialfromawhitedwarfdonor.TheEarthisshowntosetthescale.CourtesyBinSimbyRobHynes.
relativelyweakgravitationalwavesignalsincomparisontomassiveblackholebinaries,butarenumerousintheGalaxy
andeventheSolarneighbourhood.
Severalthousandsystemsareexpectedtobedetectedindividually,withtheirparametersdeterminedtohighprecision,
whilethecombinedsignalsofthemillionsofcompactbinariesintheeLISAbandwillformaforegroundsignal. This
isincontrasttolessthan50ultra-compactbinariesknowntoday. Thenumberofdetectionswillallowfordetailedstudy
oftheentireWDbinarypopulation. Inparticular,themostnumeroussourcesaredoublewhitedwarfs,whichareoneof
thecandidateprogenitorsoftypeIasupernovaeandrelatedpeculiarsupernovae. eLISAwilldeterminethemergerrate
ofthesebinaries. Thedetailedknowledgeoftheultra-compactbinarypopulationalsoconstrainstheformationofthese
binariesandthusmanyprecedingphasesinbinaryevolution. Thishasastrongbearingonourunderstandingofmany
high-energy phenomena in the Universe, such as supernova explosions, gamma-ray bursts and X-ray sources, as they
sharepartsoftheevolutionhistoryofthebinariesdetectablebyeLISA.
AsmanyoftheGalacticsourcesareratherclose(withinafewkpc),theywillbedetectableathighSNR(oftenlarger
than50),allowingdetailedstudiesofindividualbinaries. Formanyhundreds,thefrequencyandphaseevolutioncanbe
studied,enablingthestudyofthephysicsoftidesandmasstransferinunprecedenteddetail. Theextremeconditionsof
shortorbitalperiods,stronggravitationalfieldsandhighmass-transferratesareuniqueinastrophysics.
The information provided by eLISA will be different from what can be deduced by electromagnetic observations.
In particular, eLISA’s capability to determine distances and inclinations, as well as the fact that the gravitational wave
signals are unaffected by interstellar dust, provide significant advantages over other detection techniques. Compared
to Gaia, eLISA will observe a quite different population. Gravitational wave observations allow us to determine the
distancestobinariesthatarerightintheGalacticcentreratherthantothoseclosetotheSun.Thedistancedeterminations
willmakeitpossibletomapthedistributionofmanycompactbinariesintheGalaxy,providinganewmethodtostudy
Galacticstructure. Theinclinationdeterminationsallowthestudyofbinaryformationbycomparingtheaverageangular
momentumofthebinariestothatoftheGalaxy. Electromagneticobservationsandgravitationalwaveobservationsare
complementarytooneanother;dedicatedcomplementaryobservingprogramsaswellaspublicdatareleaseswillallow
simultaneousandfollow-upelectromagneticobservationsofbinariesidentifiedbyeLISA.
Anumberofguaranteeddetectablesourcesareknowntodatefromelectromagneticobservations. Someofthesecan
beusedtoverifyinstrumentperformancebylookingforagravitationalsignalattwicetheorbitalperiodandcomparingthe
signalwithexpectations. Inaddition,onceeLISAhasdetectedseveralnearbybinariesanddeterminedtheirskyposition
theycanbeobservedoptically,thusprovidinganadditionalquantitativecheckoninstrumentsensitivity.
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