,

Low-frequency gravitational-wave science with eLISA/ NGO

Pau AmarO-Seoane l.13

, SoHane Aoudia l , Stanis lav Babak l ,

Pierre BimHruy2. Emanuele Bcrt j:J ,<I, Alejandro Bolu~5, C hiara Capriniu, Monica Calpi7, N e il J. Cornis h8, Kars ten Danzmann I, Jeall-Franc;ois Dufaux2, Jonathan Gairll. Olive r J c nnrich JO , Philippe Jetze r ll, Antoine Klein 11.1:I , Ryan N. Lang l2 , Albe rto Lobo l3, Tyson Littenbe rg I4,15, Scan T. M c \Villiams 16 , Gijs N e le mansI7.18.19, Antoine Petiteau2.1, Edward K. Porter 2 , Be rnard F. Schutz i , Alberto Scsana ', Robin Ste bbins15 , Tim Sumner '20, Miche le Vallisnc rr;ll, Ste fano VitaJe22 , Marta Volonte ri23.24 , and He nry Ward2S

ll\hl.X Planck Inst. fur GravitaLionsphySik (A lbert-Einstein-Iusl. ), Germany 2APC, Univ. Paris Dklerot, CNRS/IN2P3, CEA/ lrfll, Obs. de Paris, Sorbormc I~"ris Cite, France 3Dept. of Ph}'li. and Astronomy, Univ. of Mississippi, Uuh'Crsity MS 38677, USA 4 Division of Phys. , Math. , aud Astronomy, California lust. of loch., Pasadena CA 9112:' , USA 5UP~[C-CNRS, Ul\1R7095, Inslitut d ' Aslrophysique de Puris, F·750 [4, Paris, France 61nstitut de Physique Throriqlle, CEA, IPhT, CNfiS, URA 2306, F-91191 Cif/ Yvette Cedcx, France 7Univ. of 1\lilallO Bicocca, !I'lilano, [·20100, Il aly 8Dcpl. of Phys., Montana Stale Univ. , B<Yl.eman 1\11' 59717, USA 9[U8t. of Astronomy, Univ. ofCnmbridge, Mudingley Road, Cambridge, UK rO ESA, Kcplcrlaan 1,2200 AC Noordwijk, 1'hll Nlltherionds I! Inst. of Theoretical Phys. Univ, of Ziiridr, 8057 Ziirich Swiuerlnrrd I~Washingto rr Uni\', 51. Louis, St. Louis MO 63130, USA 1~ l n~tittrt de Ci~llcies de l'Espai (OSIC-IEEC), Cnmpus U/\B, I::S·08193 Bellatcrm, Barcclolla, Srmill 141\lnryland Centcr for Fuudarnllntal Phys" Dr:pl. o f Phys .. Ull iv. of Maryla nd, College Park 1\1D 207,12 15C ravitntional Astrophys. Laboratory, NASA Cuddnrd SI}{\cellight Center, Cn:enoclt ;\,11) 20771. US,\ !6Dept. of Phys .. Princeton Univ., Princeton NJ 085·11, USA Il' D ... 'pt, of Astrophys .. Radboud Univ. Nijlluogen, The Netherlands Hl lnst. for Astronomy, KU Le llnm, 3001 Leu\'cn , Belgium I1JNikhef, Science Park 105. 1098 XC Amsterdam. The ;\'elhcr!ands lO BIackcu Lab., Imperial College. I.ondon, UK 11 Jet P ropulsion Laboratory, Calirornia Inst. of Technology, Pa/Il..:I('na CA 91109, t:S,\ l"lUlliv. of 1'tenLO. Dept. of Phys. alld I;.lFN, 1·38123 1~0\·0. l'rento, Italy 23 lnstitut d't\strophy~ique d,.. I'aris, !RluiJ; [lollle\'1'1l1:\ ,\ mgo. 75011 P"ris. Franre Ht\stronomy Dept .. Univ. of :\Iichigan. I\nn Arbor:\11 .18 109, l"SA ~:; l nSL for Gravitatiollal Research, Dept. of Phy!, &.: Astrononw Kct.-ill Building, Univ. of Gl""gow. Glasgow. UK

&rnnil: Micbele. VallisneriOjpl. nUIl.gov

Low-frequency gmvitationai-wave science with eLISA/NCO 2

Abst.ract. We review the exp.x:tt.>d :science pedOrnllHlCe of the New Cl"/witllt.ional-Wavc Obscrmtory (NCO, /l..k./l.. e LISA), II. mission under study by the l!:ul"opean SPRee Agency for launch in tile early :2020s. eLISA will sur· vey lh ll 10w-frC<llIclley gravillltioual-wllve sky (from 0.1 mlh to I liz), detecting and cllll racterizing a broad variety of systems lind events throughout the Uni­verse, induding the <XI<"l.I~nces of IlHIS.,>i"e block holes brought together by glllaxy mergers; the inspirals of stcllar-mll.lill black holes and compact. stars into «Illral galactic black holes; sc\"Crai millions of ultrllCOlllpact binaries, both detac.:hcd and mass transferring. in the Cal{lJl;Yi and possibly unforeseen some<'!! such 11.'> the relic grnvitalional-wa\'e Tll(lialion from the eMI)' Universe. eLlSA '8 high signfll­lo-noise measurements will provide new insight into the structure and history of the Unh-erse. and they will ust general relativity in its strong-riekl dynamical regime.

PACS numbers: 04.80.NII, fl5.55.Ym

1. Introduction

Over the lost two decades, as many as 2,500 articles on space-based gravitational­wave (GW) detection ineluded mentions of LISA (the Laser Interferometer Space Antenna) 11,2,3), the spact..,-bascd GW interferometer planned and developed together by NASA and ESA. This collaboration betwCCIl t he two agencies ended ill early 2011 for programmutic and budgetary reasons. in fact, LISA, as brought fort h by the entirety of those papers, was more than a space project: it was the concept (and the cherislu."d drcum) of a space- bru;ed GW obscrvatory t hat would explore the low­frequency GW sky, in a frequency band (10 - '1_ 1 Hz) popu lated by milliOIlS of sources in the Galaxy und beyond: compact Galactic binaries; coalesci ng 1ll3..Sl>ive black holes (i\ IBHs) throughout the Uuivcrse; the captures of stellar rcmnants into MBHs; and possibly relic radiation from the early Universe.

All aloug its evol ution, the LISA design remained based on three architectural principles developed and refi ned since the 1970s: a triangular spacecraft formation with ~ fkm arms, in Earth-like orbit around the Sun: t he cont.illllolis monitoring of inter-spacecraft distance oscillations by laser interferometry; drag-free control of the spacecraft around freely falling test masses, the rcference endpoints for the distllllce measurcments, achieved using micro-New lOll t hrustcrs. The current iucal'llation of t,his concept is eLISA (evolved LISA), a mission under consideration by ESA alone (under the offidul mHtle of NG O, the New Gravittttionnl-wnve Observatot"y) for IUlInch in 2022 withi n the Cosmic Vision program.

The eLISA (\t'Sign would achieve a great part of the LISA scicnce goals, as prcsent(.'(\ in [1\, ali(I endorscd by the 2010 U.S. astronomy and astrophysics decacitll [41. This article surveys eLISA's scicncc performance (sensitivity, (' \'Cltt rates, {Iud paramet.er (''lStimatiou), os scoped out by these authors in the spring and sUlllmer of 201 L and as discuSSCt"1 iu full in Ref. [5J. T his ill·tiele is organized ru; follows: in Sec. 2 we provide H vcry brief o\'erview of eLlSA and it.s GW sensitivity. while later sections are organized by science topics. III Sec. 3, we d iscuss the ast rophysics of compact stellar-mass biu[lrics ill the Gulaxy: in Sec. 4, t.he origin and evolu t ion of the mas.<;ivc BHs fo und at the center of galaxies, 1.l..'> studk'(llhl"ollgh their coalescence GWs: in Sec. 5, the dynamics and populations of galactic nuclei, as probe(1 through the cnptures of stellal"-ma:;s objects illiO lIIassive BHs: ill Sec. 0, the fundamental theory of gravitation, incJ ud illg its bcllt\\"ior ill the strong nonliUl'ur regime. its possible de\'iutions from general-relutivistic predictions. and the nature of BHs: in Sec. 7. {he (pol t:'ntially new)

Low-jre(}!teflCY gmvitational-wave science with eLISA/NCO 3

physics of t he early Universe, and the mcasurement of cosillologicul paramcters with G\V events. Lust, in Sec. 8 we draw our conclusions, uud express a wish.

2. The e LIS A mission aud sensitivity

\Ve refer t he reader to [5) for a detailed description of the eLISA architecture. eLISA has (I cleur LISA heritage, with a few substantial differences . T he eLISA urms will be shorter (1 I\ lkm), simplifying t he t rucking of distant spacecraft, alleviatiug re<luiremcnls on lasers and optics, and rcduei llg the mass of t he Jl!'Opcllant needed to reach t he final spue«.:raft orbits. T he orbits themselves may be slowly drifting away frO Ill Earth, again savi ng propella nt, and the Ilomiual mission duration will be two yems, extendable to five. As much existing hardware as possible, including the spacecraft bus, will be incorporated from t he LISA Pathfinder mission, scheduled for lau nch by ESA ill 2014. T he three spnct.'Craft will consist of one "mother" and two si mpler "daughters," with interferometric measurements along only two arms, for cost and weight savings that make launch possible with sllluller rockets dUUl LISA. (Note that LISA was to be built with laser li nks (liong the three arms, but it was not a r<"'quirement that they would operate throughout tile mission.)

The eLISA power-spe<:tral-density requirement for the residual test-mass acceleration is Saa;(J) <= 2. 13 x 1O-2'J( 1 + 10-4 Hz/ f) m'2s-4 HZ-I, while t he j>Ol:iilion­noise rt.'quircmcnt breaks up into S~,,(J) ::= 5.25 X 10-'23 m'2 Hz- l fo r shot 1I0 ise, and 50 "",,(/) ::= 6.28 x 10- 23 1112 Hz- l for all ot her measurement noises. "Vith t.hese requirements, eLISA achieves the equivalent-strain noise plotted in Fig. 1, and approximate<1 analyt ically by

S(f) ~ 20 4S~,(f) + S~(f) + S~",,(f) x (1+ ( f))' 3 L2 0.<11 c/2L '

(\)

where L = 1 Mkm, c is the speed of light , and S(/) has al ready been normalized to account for the sky-averuged eLISA response to GWs. This noise allows the detection of a strain of about 3.7 x 10-'24 in a two-year measurement with an SN R of 1. The requirement on t he llsefuimeaslll'emellt bUild is 10- 4 Hz to 1 Hz. wi th a goal of3x 10- 5

Hz to I Hz.

3. Compact binaries in t he Galaxy

The moot Ulll llerous sources in the low-frequency GW sky observed by eLISA will be short.period binaries of two com pact objects such ('IS white dwarf. .. ( \\I~s) or neutron stut's (NSs). T hese systems have weak GW emission relative to the much heavier llIHSSi\'c-I3H biuaries, but arc nUlIIcrous in the Galaxy and even in the Solar neighborhood. To date. atitronomers have obscrv(.'(\ ohotl t 50 ultra-compact binaries wilh periods shorter than one hour. L'Omprising both dctaehe<1 systcms and intt'racting binaries where mass is being transferred f!'Oll! one star lO the other. Wide-field ami synoptic ~u r"('ys such as SDSS and PTF (alld in the future, PanSTAnnS, EGAPS, (1nc! LSST) will t:OlItillue to clliarge this sample [7. 8J. Illteracting ultra·cOItlpact binat'it'S with )is aCL'rClors are found by all-sky X-my monitors aud in de<\icat('(1 sun'eys [91.

A large subset of known :.ystems will be guara nt{'(.'(1 ve rificatio n sour ces for (' LI SA [IO): their wcll-modeled GW siguals will be dete<;ted within thc first few weeks to mOlll hs of oP('l'ut iOll. "crifying instrument pCrfOl'lnilnC(>. The most prombing \'criftcatiOil binaries arc t ll{' shurtest-known-pl'rio<l il ltt'ractiug systcms H},j Cue (with

Low-frcquency gravitational-wavc science with eLISA/NCO ·1

,,- 10-,3 ; N 10-'· ;;. 0 10-'5 en Cl.

• 10-'5 E 0 eLISA, simulated ·i 10-,1

\ ISA. Eq. (1) 10-'8 0

~

~ 10-,i LI SA J

:if 10-20

10-' 1 0~ 10-' 10-2 10-' I (Hz]

Figu r e I . e!. ISA equivalent-&trllin tloi~, avet"llgL'd OW!r source sky Ioclltion and polilriZlltion, as 8. function of f!"L'Ilucncy. Tile solid red curve was obtained with tile U SACode 2.0 simulator [til, while the dashed blue curve is plotlL-d from Eq. ( I ). For comparison, t he dotted green curve !ihowil the LISA seusi t ivity.

a l>Cl·iod of 5.4 m [1 I!), V,107 Vul (P = 9.5 Ill), and ES Cet and the recently discovered detached system SDSS J0651+ 28 (P = 12 m; 112[).

eLISA will individually detect and determine t he periods of several t housand currently unknown compact bina ries (in our esti mate, 3,500-4, 100 systems for a two-year observation; [5, 14]), while t hc combined signals of tens of millions llnresolvu ble systems will form a s tochastic GW foreground aI, frequcncies below a fcw mHz ([ 15, 16]; Sl.~ Fig. 2.) About '" 500 doscor high-frequency (> 10 mHz) :;ources will be seen with large SNRs, allowing t he determination of sky position to better than 10 deg2, of fre<luellcy deri .... ative to 10%, of illclinatioll to 10 deg, and of d istance to 10%. T his large sample will allow a detailed study of t he Galactic populatioll. which is poorly const raincd by E~ I observat ions ulld theoret ical !In.-dict ions {l7].

Detect ions will be dominated by d o uble WD binaries with the shortest periods (5- 10 1lIinutes). T heir lncrgers are cand idate progenitors for Inany illteresting syst.ellls: t.ype In [18} and peculiar supernovae [19, 20[: si llgle sllbd wurf 0 ami B stars, R CorOlla Borcalis stars and maybe all mussive W Ds [2IJ: and possibly the rapidly spinnillg NSs observed as illS radio pulsurs and magneturs {22]. These bi ul.u·ies are short liv\.'<! . vcry fai nt. for telescopcs, and scarce (few thousu nd in the whole GallL"'Y), so CWs will provide il uniquc wi ndow Oil their physics. eLISA will detcnniuc their merger rote , collstmi n thei r form ation. and ilhull inote t he preceding phases of binary evol ution, most notably t he colllmon-em·elope phase.

Common-e nve lope evolution is cruci<ll to most binary systems t hat produce high-energy phenomena such as ~I-ray bursts and X-ray {'mission. but our lIu<it'rstallding of its physics and outcome is limited [23. 24] and ehallcngt..'f.\ by obSCf\1ltions [25. 26]. The stondard scenario is as follows. ~ Iost stan; in the Unhwsc are in binari(>S. ali(I roughly half of binaries ure formed at. close e!lough separarions that. the sturs will interact os they evolve into giants or su pergiullts. Following runaway nlflss t !"unsfer. the ('olll]lmdon of the giam con eud lip illside the outer layers (the ('m"('lop<') of !.he ginllt: dYliamical frictiou rcduces the ,'elodty of the romp/lllion,

Low·l,.eqrumcy gravitatiollal-wave sciellce with eLISA/ NCO

1 D-'" N l-year time series, ~ residual foreground

• rJ; 10"" o '" 00

• _____ 0 - ... -...-,

1 Q-I2 inst. + coni. Af/I)IIdJo'\r" 'Y

inst.

10-" 10~ 10~ 10~

I [Hz[

5

Fig ure 2 . Main figure: I)()\\'(!r spec:trnl density of the stochastic CW foreground from Calnctic binaries, fH!fore (blue) (Iud after (red) the lIubtraction of individually resolvable systcms, which 1.re ploUed ns green and red/bluc dols (for detacbc<l und ml'L6S-tmnsferring systems). A few known verification bina ries are shown as white dots. The solid / dashed block curves t race inlltrument noise alone/ wilh confusion noise. Spectra are shown forthe TD I ob!;el'w.ble ~X" (see, e.g., [13/); lIubtrnction is simulated for a lv,'O-year observat ion and threshold SNR = /; resol\ll\ble systems nre pJncec:l 1\ foctor SNR'l above the coUlhino."(1 instrument a nd confusion noise. Inset : litHe seri~'!I of the residual foreground. which curries inFormution ubout lhe II llinher l.lId distribu tion of binaries in the Galaxy.

shrinki ng t he orbit and transferring angular momentum and energy into t he envelope; the cnvelope eventually becomes unbo und , leading to a very com pact binary consisting of the core of tlte giant and t he original compauion [27J.

cLlSA will also test dynamical interactions in g lobular clus te r s , which produce an overabundance of ultm-compact X-ray binaries consisting of a NS accret ing material from a WD companion. The eLISA angular rcsolut.ion will be sufficient. to dist inguish WO binaries in clusters, \'erifyi llg whether t hey arc also plentiful.

The eLISA measuremcnts of individual short~period binaries will provide a wealth of inrormation 0 11 the physies of tidal imeructions (Iud the stability of mass transfer. For dctached systems with little or lIO interactioll , the evol ution of t.he GW signal is dOlllllw ted by gravita tiol lul I'lldiation:

(2)

where II is t he GW strain. f t he GW fl'L'<IIlCIICY. ;\1 = {lIIllnzfi/"/(ml + m2)1/5 is the chirp mass with 1111' 1Il2 the illd ividual IllHSSes, and Dis Ihe distauce. Thus. meHsuri ng II, I , and j (which will Ix> possible in 25% of systems) p!'Ovitk'S ... \.1 and 0: tucnsllri ng also I (which Ina), be possible for a few high-SN R systems) tests s(>ClIlur effects from tidlllllnd mass-tnulsfcr imeructions. Short· term variations are lIot likely to prc\'l'ut delection [281. aud the prC'Cision of j and j dCl crllli nation increases with Ihe d uration of I he mission.

Low-fi'Cqac'lCY gmuitatio"al-wave science witJt eLISA/NCO 6

T idal in teract io ns are pos.o;ible when at. least aile binary c:omponellt docs not corot ate wit h the orbital Inot ion, or when t he orbit is ecccntric. T heir streng! h is unknowu [2!J], aud has irnpol'tant consequences 0 11 the tidal heutiug (and possibly optical observability) of \-VD binaries, as well as the stability of mass transfer . T his process begi ns after gravitational rad iation shrinks detached binaries !o sufficiently close orbits (with P ..... a few minutes) that. one of t he stars fills its Roche lobe and its material ctln leak to til(' companion. Mass transfer can be self-limiting, stable, 01'

unstable, depend ing 011 the result ing evolution of the orbit and of the donor radius. Unstable transfer leads to mergers: stable systems (the interacting WD binaries known as AM eVn systems, as well as ultra-compact X-ray binaries) will be observed - and counted - by eLISA in the early stages of lllass transfer [30]. Efficient tidal coupli ng can return angular momentum from the u.ccreted material to the orbit [29, 31, 32], slowing the inspiral and increasing the frac t ion of WD binaries that surv ive t he onset of mass transfer from 0.2% to 20% [33].

T he unresolved foregro un d from Galactic bi naries will provide a light addit ional noise com ponent. for the detcction of loud broad band signals (see Fig. 2), but it also contai ns precious astrophysico.l infonnation. Its overall level measures t he total number of binaries (mostly double WDs); its spectral shape characlel' i'l.es t heir history and evolution; and its yearly mod ulation [34J, togethcr with the distance determinations from Ulany individual systems, constrains the distribution of sources in the d ifferent Galactic components. T hus eLISA will probe dynamical effects in t hc Galactic center, which may increase t he number of tight binaries 135}; it will mca.<;\Il'e t he poorly known scale height of the disk; am.l it will sample the populat ion of t he hulo [36, 15], which hosts two anomalous A~'! eVn systems and which may have a rather different compact.-bi nary population than the rest of the Gu1axy. Furthermore, t he eLISA measurements of orbital inclinations for individ ual binaries, compared wit.h the overall angular momentu m of the Galaxy, will provide hints on the formation of binaries from interstellar clouds.

eLISA will also constrain the formation rate and numbers of NS binaries and ul tra-com pact s t e llar- mass B H bi naries , t hroughout the Galaxy and without E~ !

selection effects. These lIIunbcrs are highly uncertain. but us lIlany as several tells of systems may be detcctable by eLISA [33, 37}, complementing the ground-based GW observations of these sallle systems in other galaxies (and at much shorter periods).

-"lore generally, t he as t rophysical populations (I ud parameters pl'Obed by eLlSA will be differcnt frOlll , and comp1ell lentary to, what can be ded uced from E~ I

observntiOIiS. For instant.'C, eLISA will be sensitive to binaries at t he Galactic ceuter and throughou t the Galaxy, while GAlA 138] will be limited to the SainI' neighborhood; C Ws en<."O(\e distances and orbital inclinations, while E:\ ! emission is sensiti\'e to surface processes. Dedicated obsen'ing programs and public datu releases will ullow simultancous and follow-u l> E!\ ! observutiolls of binaries identified by eLISA.

4 . Massive b lack- hole bi na ries

(See [5] for u nmch deeper review.) According to t he accretion parad igm [39. 40. "' iJ. supermas..;;ive 131-1" of 1()6 109 J/p power quasars active gulactic nuclei so IUllliuous that. they often outshi ue their galaxy host. whieh are detl-'Cted over t he entire cosmic time acccss.ible to our !cicscopcs. Quiet sU I>crmassi\'e BHs are ubiqu itous in Olll' low­redshift Ulliverse, whel'e Ihey arc obser\'ed to have musses closely corre!ute<l with key propcrtit-s of their galactic host. (see [42]. uud refs. therein) lcading to the no! ion thaL

Low-frequency gmvitatimwl-uJave sciefloo wiilt eLISA/NCO 7

galaxies and their nuclear ~IBHs form and evolve in symbiosis (see, e,g" \43, 44, 45]), In t he currently favOf(,'(i cosmological paradigm, regions of higher-density cold

dark matter in the early Universe forlll self-gravi tating halos, which grow t hrough mergcrs with other halos a nd accretion of surrounding matter; baryons {Ul(\ ldBHs arc thought to follow a similar bottom-up hierarchical dusteling process [46, 47, 4S, 49, 50], ~ IBHs may be born us small seed.9 ( 102_103 M0 ) from t he COfe collapse of t he first generation of "Pop III" stars fOfmed from gas clouds in light halos at z '" 15- 20 [51,501; or as large seeds ( I03_ lOS .?!l0 ) from the collapse of very nHlssive quasi-stars fO l'llIed in much heavier halos at z "" 10- 15 [52, 53); a t' by rUlJaway collisions ill star cl usters [5<11; or again by dircct gus collapse in mergers [55) (Sec [56, 571 and refs. therein). T he seeds thcn evolve over cosmic t ime through intermittent, copious accret ion and through mergers with other MDHs after the merger of their galaxies.

The cosmic X-ray background from acti ve MBHs at z < 3 suggests t hat radiative!y efficient accretion played a large part ill bu ilding up MBH mass (58, 59, 60), so information about the initial mass dist ribution is not readily accessible in the local Universe, Dy contrast, eLISA witl measure the masses of the original seeds from thei r merger events. Fu rthermore, it is unknown [61 ] whether accretion proct.'C<ls ClJlie,-ell tly from It geometrically thin , corotati ng disk (62] (which cun spin ~ ... lBHs up to the J 1M2 = 0.93-0.99 lim it imposed by basic physics 163, 64]) or chaotiClllly from raudomly oriented episodes [65) (which typically result ill smaller spins). eLISA's ac(; urute measurements of r-,·IDH spills will provide evidence for either mechanism [66].

After a galact ic merger, t he cClltral !-. IBHs spiral inward , together with their bulge or disc, under the action of dYllll mical frict ion, and pair as a pc-scnle Kepierillll bi nary 167, 6S, 69, 70, 71J; ~ I BH bilwries are then thought. to hanien into gravitational­rad iation-dominated syst.ems by ejecting nearby stars (assulIlillg a sufficient supply) [72,73, 74] or by gas torques and flows ill gas-rich environments [75, 76, 77]; the final bi nary coalescellce is t he most luminous event in the Universe (albeit in GWs). BH mergers haye been explored only recently by Illilnerical relativity 178], showing how the mass and spin of t he fi nal BH remnant arise frOIll those of the binary components, and pred icting remarkable physical phenomena such u.'1 large remnant recoils for peculia r spin configu rations [79]. T he pred ictt.'(1 coalescence rate in the eLISA frequency band ranges from u ha nd ful up to few hu ndred evellts pe r year, dcpend ing on theoretical assumptions ([SO, SI , S2, 83, S-I , 85, S6, 87]) .

eLISA will be sensitive to GW signols from HI! t hree plutSes of MDH coalescence (inspiral, merger, aud ring.down 188]). To assess the eLISA scicnce performance ill t his area, after ex perimenting with different wa\'('fol'l1l families. we modeled these signals with the "PhenomC" phenomenological waveforms [SD], which st it.ch together posl.·Newtonian (PN) inspira] waves [90] with fre<plCncy-domain fi ts to lIulllerically modeled hlte-inspiral ami ri llgdowJl wu,·t.'S. (PhcnomC \\'avcforms wcre deriycd for binaries with aligned spi ns: we adapt them to t he Ilon·aligne<l case by projecti ug t he orbit al lI ngular momentum lind ind ivid ual spi ns allto the angular momentum of t he distorted BH after merger.)

T he first metric of performance is the detection SNR. angle-a\-crage<1 O\'er sky pooition and source orientation. which is plottt.'!1 in F ig, 3 as a function of total rcst lIIass aud (;osmological redshift (left pancl ) aud as a function of total rest mass aud Itl lL'iS ratio for bi naries at ;; = 4 (right panel), eLISA c:ow:rs al lilost all t he mass I'cC\shift parameter space of ~IBH ast rophysics: any e<lual-mass binary with ,\ll o~ - 10-1 10' ,\I, (the crucial "middle\\,f>ight" rnnge inaccessible to E~ I obscrvations beyond t.he local Uni"ersc) call be detected (with SKR > 10) out to t he highest

Low-frequency grnvitatio11lli-wa've science with eLISA/NCO 8

20

18

16

14

." E ~ 10

~ 8

6 , 2

2 3 ,

H' ,0' •

• • • H" . , • • , z , 0

W

>C.

0

0.5

! 1.5 '!i ~

2

2.5

z = 4 5 6 7 8 9 10 2 3 , 5 6 7 8 9 10 1og ",(M.c.IMo) Iog' G(M.lM~)

Fig ure 3. Left. : collStllnt-lc\'el conwurs of sky- and polarl7.ation-an~_raged SN it for CQual-m_ non-spinning biuaries as a function of tota l n.'!i t mass /llto~ 1\nd oosmologic1\1 redsllift z. TIle SNit includCl> inspirnl, mergl.-1" lind ringdown . Rig ht : SNR CO"~Olll1lllli n function of /!Ito. !lnd 1111186 ratio q = ml/m2.

0.'

03

/Sky-avera9OO SNR. equal·mass ~ 02 M.. ,. lO"M binary

'. '.

'" ~ -. -'" ---- 0.'

, 'i0%. 90% perCljl"ltiiea

0 5 >C " 0

0 02 O. 0.' 08 redshift ~ ,

Fig ure ,I . Left : d istrilllJtion o f expected SNit for il.1BH mergers !OS a function of Z, COml)uted from the SEI LEISel Le lIlctl\C!l.talog (see II1l1in text). Rig ht : likelihood for the mixing frllcl.iOJl F, for an individu,'[ n :n1i'l!ltion of mixed lI10del F SE + (\ - F) LE with F = 0.45 (see main text).

redshifts, while equal-muss biuaries with J!tOl > 105 M . are seen in detail ,L~ strong signals (SNR > 100) out. to z = 5. Biuuries with Mlot > 10" ,U0 and mass ratios;S 10 are seen wil h SNR > 20 ou t to z = 4.

To ('vuluute expected S~Rs in the context of realistic MBH populations, we consider four fiducial scenarios (SE. LE. SC, LC) \\·hcrc ~IBHs originally form from S mall (- 100 .\I",) or Large seeds (- 105 .\l .J. and where t hey subseclucntly grow by Extended or C haotic accret ion . (SC(' [9 1] for details; here we enhance that analysis by incl uding random spill orbit tnisalignltlents up to 20 <leg in E models [92]). For each scenario we generutf' multi pic catologs of merger events, a nd join them in equal proportions iuto a single mctacatalog. Figure 4 shows the resulting distribution of S~R with .:::: eU SA will dctf'Ct :;Qurte> wit h S:"R ~ to out to.:::;S 10. a limit imposed b.v mUSS(>S of the expectNI binary population as a fUllctioll of .:::.

For t he Same metncll1.o1og. Fig. 5 shows the expected accuracy of parame t er determinat io n , ('st inwtcd using l.l Fisl\('r-matrix opproach based 011 P:\" inspirai

LotJr-jrY!f/llency gTnvitatiOlwl-waue science with eLIS A/ NCO 9

{ -- ~ , , , •

109.Jlim,lm,)

. •

tOM ' .

~

1 r'

J I ~ • ., ., ., • H ., • , , , • ,

1Og , ,~/m, 1 1Og,.(60:dl>g'l

Figure 6. Pflramcter-estimatiou a«:uracy (relative frt.'(lucncy of frllctionfl! or absolute errors over SEILElselLe I1lchl<:1Llnlog) for primary nml o>econdnry n;dshifted M 1311 IllIlSS('!:l and dimensionh."SI:I !mins (m Land m2. a L 1m I nnd 112 / 1112 .

respectively), lumiuosi ty distance DL and sky Il,osi tiou ~O.

waveforms wit h spin-induced precession, augmented with PhcnomC lllerger-ringdown waveforms. eLISA cun determine the 1"f!l/.<J/tijted componcnt masses (mredshift = ( 1 +z) fIlr""d to 0.1- 1 %, thc primary-l\'IDH spins to 0.01 - 0.1 ; auci the scc.;ondary-l\ IBH Sl)ius to 0.1 in a frac tion of systems. (Compare with E1\1 t>. IBH-muss unccrtainties '" 15- 200%, cxcept for the l\ lilky Way l\ IBH, a nd wit h very large l\ IBH-spin unccrtilintics from KO' iron line fi ts [93J.) The errors in DL have a wider spread , from a few percent to virtualllon-deterrnillatioll , while sky position n is typically determined to 10 1000 deg2. Compiu·(."{1 to previous published estimates for LISA, the accuracy in determining both D /. and n is reduced for eLISA by havi ng interferometric measurements only along t\VO arms (although t.hree arms were alwa:ys a goal, not a requiremeut. for LISA).

T he next order of analysis is to (.'Ombine 1I111lti pic MBH+coalescence observations, resulting in a catalog of binnry/ l'cIl1llunt parameters, into a single inference about. t he mecha nis ms of MBH fo r mat.io n a nd evolut ion t hroughout cosmic history. This problem was analyzed extensively by Scsana and (.'Olleagucs [!).I) in t he context of LISA. We repeated t heir analysis for eLISA, by generating 1,000 catalogs of detected mergers (over two years) fo r each of t he fo ur SE/ LE/ Se/ Le scenarios, ali(I comparing the relati"e likeli hood p(A vs. B ) = p(AIC) / lP( AIC) + p(BIC) } for each pnir of scctwrios (A , B ). fol' C = A or B. We considcred only detections with SNR > 8, ami used spilliess, restricted PN waveforms. Table l shows our results for a relative likelihood t hreshold 0.95: for instance. t he first row on t he left shows t hat if SE is true. it couttl be disc,-i",iIWICti from LE ami LC in 99% of rcalizotions, but from SC only in 48% of rcolizations: t he last row on t he left. shows t.hat LC COl/lei not be ,·u.leti Ollt in 2% of realizations whcn SE or SC arc tnw. but in 22% of realizations when LE is true. Th is degclleracy between accretion mechanisms is an artifact of rhe spin-less assum ption: iuciuding information about the spi n of rhe fi nal merged ~IBH (which can be mcas ured in 30% of detections) provides essentially perft.'Ct discrimination.

Last , because no theoret ical model will exactly cnpLllre the "true'· formatiou !.Iud evolution history of .\IBHs. we investigated eLISA's ability of IHc;LsllrilJg the mi:l"i llg fraction 0 < F < I in a m ix ture mode l FA + ( I - F )B t hat produces coalescencc e\·C'nts with probability:F from scellal'io A. and I - F from B. For instalL(.'t'. for the ca..e E SE + (1 - F )LE wirh F = 0..15. F can be measured wit h an uncertainty of 0.1 (sec right panel of Fig. 4). Although highly ideolized , th is cxample shows t il(' potential of eLISA's obscrwltions to constrai n .\I8H astrophysics aloug thei r ent ire

Low-jreqlle'lCY gravitational-wave science with eLISA/NCO 10

Tob ie l. i\lodcl di8CrimiualiOIl with eLI SA !l.IB Il-binary ohscr\'J\liOJl~. The upper-right lu.lf of each table shows thl.) fraclion of realizations in which tile row lUodel would becho:;;ell over the co/urn" 1I10dei with a lik,dillood th reo;hold"> 0.95, whe ll the row model is true. The lower-left half of each table ShOWN the f!"!letio!! of rca lizatiolls in which the row mo<id call not be rnled om against the w/um,z model when the column model is true. In the left table \\"(1 cOlisider only the men';lUred IlI/l..\iSC$ !Ind r005hift for obiwrv(!(1 <,''Cnts; in the right tnble we include also the observed distribution of Il:!lU IIIllit spins.

without Silins wi th spins SE SC LE LC SE SC LE LC

SE x 0.48 0.90 0.99 SE x 0.% 0.09 0.9<J SC 0.53 x 1.00 1.00 SC 0.13 x 1.00 1.00 LE 0.01 0.01 x 0.71) LE 0.0 1 0.01 x 0.97 LC 0.02 0.02 0.22 x LC 0.02 0.02 0.00 x

cosmic history, in muss and redshift ranges inaccessible to E i\1 astronomy. In closing t his section, we note that eLISA may also detect ooalcscences of BHs

with masses of 102_10'\ Me (intcrmed iate-muss DHs, or 1i\ IBHs). These events do IlOt result from hierarchical galaxy mergers, but they occur locally under the cxt reme conditions of star clusters. UvlBHs may form in young clusters by way of mass segregation followed by runaway mergers [95, 96 , 97, 98, 99]; IMOH binaries may form in Si t11 [100], or after the collision of two cl ust~rs [101 , 102J. Although the evidence for IMBHs is tentative [103, 104], eLISA lIlay observe as lllallY as a few t'OalcscellCes per year [101) out to u few Gpc [89J; it may also clet.ect stellar-mass BHs plunging into H\'!BHs in the local Universe [105).

5 . Extreme-muss-ratio inspirals and t he ast rophysics of dense ste llar systems

There is of course olle galactic nucleus. our ow n, that eun be studied and imaged ill great detail [106, 107, 108, 109, 110, 111). The central few parsecs of the r-Iilky \Vay host a dense, luminous star cluster cell tered around the extremely C01UPlict radio source SgrA· . The increase in stellar velocities towtll"d SgrA' iudicat(.'S the presem.:c of u (4 ±O.4) x 106 !'lIe central dark muss [Ill ). while the highly eccentric, low-periupsis orbit of young star 52 requircs a central-mass density> 1013 Me pc- l [112]; u density > 1013 M e pc- 3 is also inferred from the t'Olllpnctncss of the radio source [113). These limits provide compelli ng cvidcnce that. t he dork I)oi nt-mass at SgrA" is an !'I IBH 1112, 11<. 1151·

Unfortu nately, the ncarest extcrnal galaxy is 100 times farther from Enrth than SgrA" . and the Ilcnresr quusar is 100,000 times fa rther, so imaging other galactic ccnters is prohibitiw·. It will howeycr become possible with eLISA. This is bl.'CHUse

!\ IBHs arc SUf\"o ll11Licd by 11 Hlriely of stellar populatiolls . including compact stelli.ll" rcmnants (stellur BHs, NSs, ulld WDs) thaL cnn reach \'cry relativistic orbi ts I.ll"Qund the 1\ iGH without bei ng tidally disrupted [1161. T h\"' compact stars tllay plullge di rect l.r iuto the CVClIt. horizon of t he ~IBH; or the.r may spiral ill gradually while emittillg CWs. These lattcr systems, known as extl"cme-mfl,~.9 mtio ill$pir(lL~ (E~IRIs) . will prod uce signals dctI..'Ctahlc by ('LISA for ~IiOH masses of 10""' 107 .\1 .. Stellar-mass DHs should be concentrated in CIISPS !l(>nT :\ IBHs jI 17, 118, 98, 119. 1201 and generate :;trongN

LQw-/1f;quency gmvilalional-1lJave science with eLISA/NCO 11

GWs t hanks to their relatively larger muss, so they will provide most detections. E i\ !RJs arc produced when compact stars in the iuner 0.01 pc of galactic nuclei

arc repeatedly scattered by other stars iuto highly eccentric orbits whcre gravitational radiation takes over thei r evolut ion [116]: resonant relaxation caused by long-term torques between orbits increases the ratc of orbit diffusion [121 , 122], although relativistic precession call hinder this mechanism [123]. E~'IRls can also be made frolll t he tidal disruption of binaries that pass close to t he i\II3H [124], pOl)Si bly ejecting the hYPcl'vcloci ty stars observed in our Galaxy (see, e.g., [125]); and from massive-star formation and rapid evolution in the i\ IBH 's accretion d isk [126]. Different mechuuiSlns will lead to d ifferent EMRI eccent ricities and inclinations. evident in the GW signal [124[.

The detection of even a few Ei\·!RJs will provide n completely new probe of dense stellar syst.ems, characterizing the llH .. >(:hanisms that shupe stcllur dynamics in the go.lactic Iluclei, and recovcring information about the MBH, the compact object, and t he EMRI orbit with unprecedented prt'Cision [116]. Especially CQvcted prizes will be accurate masses for 106_107 A10 ~'IBHs in small, lion-active galaxies, which will shed light on galaxy- !-. IBH correlations at the low-mas..:; end; l\IBH spins, which will illuminate t he IllcchaniSIll of MBH growth by mergers and accretion (see Sec, 4); as well as stellnr-BH 1IIUSS(.'S, which will provide insight on stellar formation in the extreme cond itions of dense galactic nuclei. The key to measurement precision is the fact that t he compact object behavcs as a test particle in the background i\ IBH geometry over hundreds of thousands of relativistic orbits in a year; the rt.'Sulting GW radiation encodes the details of both the geometry lind t he orbit [127, 128, 129, 130j.

To assess t he eLISA science performance 0 11 EIVIRIs, we model their very com plicated signals [131] usi ng the Barack Cutler (BC) phenomenological waveforms [132/, which ure not sufficiently accurate for detection, but capture the character and com plexity of Ei\ IRJ waveforms. \~'e complement. this Hnalysis with more realistic Teukolsky-based (TB) waveforms obto.ined by solving the perturbative equations fo r the BH geometry in the presence of the inspiraling body [133]: these have bccn tabulated for circular- equatorial orbits and for some values of MBH spin [130, 134].

To evaluate expected Ei\IRJ detection horizons and detection rates, we perform a i\ lonte Carlo over 500,000 realizutions of the source parameten;, taki ng i\IBH rest Illass ill [104,5 x 106] Me with a uniform 10gM. di!:itribution; i\IBH spin uniformly in [0,0.95]: compact-body lllasS of LO M0 , representative of a stellar-mass BH; orbit eccentricity before t he final plunge uniformly in [0.05,0.4]; and all orbital angles and phases with the a ppropriate uniform distributions on t he circle or sphere, with an equal number of prograde aud ret rograde orbits. \\'e take the poorly kllowlI E;\IRI foruwtion fflte to scul" with l\IBH mass as 400Gyr- 1(M. / 3 x 106 M0 )-O.19 [135, 136.137], lJlH[

we distribute systems ulliforl11iy in comoving volulIIe. Our assumptions are consistent with the :\ IDH muss fUl lction derived from the obsern'(l galaxy luminosity function lIsing the .\f. u relation, and excl uding Se-Sd galaxies [138, 139, 13,11.

We furt her assume un observut ion ti me of two years. consider E:\I RI s in the last five years of their orbit [134]. and require u detection SNIl = 20 [1'10, 1·11, 1<1 2]. The left panel of Fig. 6 shows the resulting III(J,rilllllm horizon redshift for DC waveforms. as a function of :\ IBH rest. mass- that is. it shows the z at which 8n optimally orientl_-,<l source \vith the most fa.\·oruhlc :\IBH and orbit pafflnu.'ters (as found in the :\Ionte Carlo) achie\'e5 the detection S~R. Th' I:':. E:\I Rls in t he ('LISA rallge will be delt.'Clable as far z 0.7, By contrast. E~I obscrvat ions of 10 1 106 M0 ~ lBl-fs are possible ill the local VIIi\'ersc Ollt to z :::: 0.1. T he l'igllt panel plots the distributiOl' of S~Rs us H

Low-frequency grnuilalional-wa,ve scirnce with eLISA/NCO 12

0.6 , ~ OA ~

02

0, averaged horiZon z. TIl , 6

Iog,.(MJM.J

,

maximum SNR. BC wavefams

M ------------------

"0\-~'0<.2'~"0 •. '~'0'.6"~;l0'8 ledshift z

Figure 6 . Le ft. : rllaxirnum horiZOIl 1'l.loshift liS. MBH rest mass. Be waveforms (n!d curve); averaged horizon rcd shift vs. ~ 1 13 11 rest rn~, 1'8 w!lvcforrn.~ with u. IM. = 0 Rnd 0.0. AssUrnl)liorrs are given in the nmin text: the rnax;rnurn is computed as the highL'St z with SNit > 20 in II. giverr mass bin. Right: mRximum E~l1U SNR vs. rooshifl, Be w!"'cforrn~.

function of z, which shows that nearby EMRls in t he local Universe will yield SNRs of many tens.

For colllpurison, the Icft panel of Fig. 6 shows also the horizons computed wi t h sky- and orieultltion-averaged SNIts, us ing T B waveforms from circular-equatorial orbits with l\ IBH spins a. / ll1. = 0 and 0.9. T he difference between t he BC and T B curves is cOIH:iistcnt with t he effects of skY-lweraging: SNIls for optimally oriented systems are ex pected to be 2.5 times higher t ha n averagcd SNRs. The a. /A!. = 0.9 systems are favored because high MBH spi n allows for orbits closer to the CVCllt horizon and higher GW frC<jHe ncies, which shifts t he peak eLISA sensitivity to highcr masses.

T he resulting number of expected eLI SA detections over two years is "" 50, as cvaluatc<1 wit,h the BC-waveform Monte Carlo, and"" 30/ 35/ 55 (for a. /A!. "" 0/ 0.5/ 0.9), as evaluated with T B-waveform sky-averaged horizons. T he higher TB event rate is explai u(.'(1 by the inclusion of eccent ric systems, which rad iate more energy in the eLISA buud , and it should be more I'eliable because of the broad sUlllpli ng of source pamille ters. Rernember however that Ei\ IRI rates are highly uncertaill [116, 135, 136, 123J. Even with as few as 10evclIls, the slope of the 1'IBH In3l;S func t ion ill the 1O.1_1OG M0 range cun be dctcl'miucd to 0.3, t he current level of observational uncertainty [1431.

Because Ei\ IRI waveforms are such eomplcx ami sellsitive functions of t he source parameters, these will be estimatl,'(l accurately whellever an El\ IRJ is det(:cted [140. 141. 1-121. In purticular. we expect to meusufC the i\IBH lIlass and Sl>ill. as well as the compact-body mass and eccentricity 1.0 betler than a part in 103 [1321. As all example. Fig. 7 shows the posterior distributions ofl lie best-determined parameters for a z = 0.55 source detected by eLISA with SNR = 25. as computed with the l\ larkov Chain Jldonte Carlo olgorithm of [14-1]: for Ihis source. the luminosity d istallce DL would be determined to 1%, and the sky location to 0.2 deg2

. Even with relali\·cly low Si\" R, pilwJ'Ilctcr-l,'Sti lllatioll accuracy is cxcelletlt. III gCIlC'ral. we filld that the eLI SA und LISA paranll'tl)r-cstiuHltion performance is very similar for Ei\ IRls detected with the :;ame SNB (hu! of course different distances). so t he reader can refer to I !'('atmems for LISA in the litcruture [132. f.l 5. 146. 142J.

Low-fHH/uency gmvitatio1l.al-wave science with "LISA/NCO 13

(M . ... - M.""')IM . .... ja.IM. )"'-(sJM. )-

-,.10" -Sxl0" a S~ 10·· 1_10"" ---6x10" -3, 10" 0 3x10" 6,10'·

(m'"'-m-j/m""" 6""-"-

F igure 7. POIitcrior probability 1)1ot for !IOurce I)ll.mmetertl (M BII rt.'SL ml.l88 III. , ~IBH spin a. , compact-body mass III, and orbit eccent ric ity at plunge e), in the SN it "" 25 detect ion of a 10 + 106 M0 EMRI at z '" 0.55, with 0. /1'.,. "" 0.7 fUld epl""IIC 0.25.

6. P recision measureme nts o f strong gr avity

Einstein 's theory of gravit.y, general relativity (GR) , has bccn tested rigorously ill t he Solar system and in binary pulsars [147. 1481; the;e tests, however, probe only the weak-field regime where the characteristic perturbative parameter € = 1J2/c? '" GAI/( Rc2 ) is very small, ....... lO - G_lO-1i (here v is the velocity of gravitati ug bodies, AI til('ir mass, and R thei r separa t ion). By contrast, eLISA's GW observations of coalescing ~IBHs (Sec. 4) and of E:o.lRls (Sec. 5) will allow us to confront GR with precision measuremcnts of its dynamical, st rong-field regi me, and to verify that astrophysical BHs arc really the Kerr mathematical solut ions I)rcdicted by GR.

Before collsidcrillg the GR tests I>ossibie with each of these sources, we Ilote t hat, by the second half of t his decade, sccond-gelU)rutioll ground- bused detectors arc expccted to routinely observe the coulesccnces of stellar-muss BHs and (possi bly) of ru;ynunetl' ic systems such as a NS inspimling into a 100 MG) BH. HO\\'cver, they will do so with 10 100 times lower SNRs than cLISA (for t he brightest sources). and for up to 1.000 times fewcr GW cyck>s; t hus. {'LISA will test our understanding of gruvity in t he Illost extreme conditiolls with a precision Ihat is two orders of magnitude better t han that achie\1lbJe from the ground. (Although most of the refercnces citcd in the rcst of this section were dc\'elopcd foJ' LISA , t heir broad conclusions are applicable to sourC('s detected wi th com parable S~Rs by eLISA.)

All three phases of ~IBH couk'Sccnce offer opportunities for precision meusurC'lllcnts. The year-long inspira l s igna ls can be cx[uuined for evidence of u massivc graviton. r<'Sulting in a frequency-dependent phase shift of the waveforlll. imprqvillg curreut Solar-systcm bounds II<I!}. (50): they eilll yield stringenl. constraints on otiwr t heories with deviations from Gn pOnllllctr izl.."(i by a S<'t of global parameters, such os mussless and Itu1.'i$jy(> Brans- Dicke theories \151. 1521. t'hcories wil.h an evolvi ng gravi tat iona! eollsttlnt [153). Lorcutz-violitting modifications of G R [154]: last. \'ariOllS aut hors haw considerC'<i testing inspiral WH\'CS for hypothctic1.l1. gellcric modificatiolLs

Low-!J-equency gl'Uuitotionoi-lIIave science witll eLISA/NCO 14

of their amplitude and phasi ng !I55, 156, 157. 158]. The me rge r of comparable- mass i\ IBH billack'S produ(."Cl> an enormollsly I>owerfui

GW burst, which eLISA will measure with SNR as high as n few hundred , even at. cosmological distances. The l\IBH masses oud spin can be determined with high accuracy from t he imipiral waveform: givclI these physical parameters, nUlUcrical rein! ivity CIl.n predict the shape of the merger waveform, as weB us the ll'lllSS unci spin of the final remnant i\I8H [159]. and these can be compared d irect ly with observations, providing un ideal test of pure GR in a highly dynamical , strong-field regime.

The frequencies and dampillg tilllt.'5 of the quasinormalmodes (QNi\ls) ill the final ringdow n [160] arc <."Ompletely determined by the mass and the spin of the remnant, and therefore can be used to me1.\sure them [161, 162], while their relat ive amplitudes hold ill formation about the pre-merger binary [163], agaill providing a check of cow;istency between Gil pred ictions for the phases of coalescence. Furthermore, the measurement of at least tv."O QN!>.ls [162] will test the Kerr- ness of the MBH [16'1] ag!li nst exotic proposals such as boson stars and gravastars [IGS, 166, 167, 168]. i\lodifications of GR that lead to different emission would also be apparent [169, 170].

EIvIRIs arc expected to be "cry clean astrophysical systems, except perhaps in fcw systems with strong interactions with the accretion disk [171, 172, 173], or with perturbations due to a second nearby MB H or star [174, 175]. Over day-long timcscales, EMRJ orbits (Ire essent ially geodesics of the background geometry; on longer t imcscales, the loss of energy uud angular momentum to GWs causes a slow change of the geodesic parameters. In the last few years of their evolution , as observed by eLISA, E~rRl orbits ure highly relativistic (R. < 10 R. ) and display extreme forms ofpcriastroll and orbital plane precession. Indeed , EMRI GWs encode all the mass and current multipolcs of t he MBH [127, 176]. which for a Ken BH are uniquely determined by t.he mass and Spill alone (another mauift:.'Statioll of t he "no-hair" theorem). For EMIUs with SNR = 30, eLISA will mcasure mass and spin to u part in 103- 10.' , und t he nulSS quadrupole mOlUcnt 1\12 to u part in 102- 10" , thus testing the no- ha ir t heore m directly [129]. See 1177, 178] for reviews of different ways to test the nature of astrophysical BHs.

Other tests of the Kerr-ness of the centrulmassive object have been proposed: for a boson star. the E1-. IR I signal would not shut off aft.er the lost stable orbit [179]; for a gnwast,ar, QI\i\Is could be excited resonant ly [168]; for certain non- Kerr axisynunet,ric geometries, orbits could become ergodic or experience reson!).ll<."CS [180, 181]: for "bumpy" BHs, orbits would again carry disti nctive signutures [127. 182, 183, 184]. Modifications in E)'I£U GWs would also arise if the t rue t heory of gravity is in fact differe nt from GR, as art' dYIiUlnical Chern-Simons theory [185. 186]. scular tensor theories (with obsel"V'.lble effects in KS BH systems where the KS curries scalar charge [151. 187]) . Rundall SumirullI-illspircd bralleworld lllodeis [188. 189], t ht.'Ol·ics with a.-..;:iO ll:; that give rise to "floating orbits'· [100, 101]. as \\·cll til; gellel"ic, plumomenologically parametrized theories [192J.

7. Cosmology a nd new physics fro m the early U ni verse

GWs produced after Ihe Big Bl.lllg fonn a fossil radiation: expallsion pre\'ent,~ them from rcaching t hermal l'quilibriutll with the 01 her components because of t he weakness of the g,nn-itational i!lteraction. Thus, relic CWs caITY infonllatioll about the first illf:tants of the Universe. If their wavelellgth is set by the apparent horizon size el f{. = c(lll it). at liu.' t illle of production. when til(' tcmperulure of the Uuiwtse

Low-frequency .tJlnvilatiolwl-1Uave .science with eLISA/NCO

eLISA sensitivIty

G -10-" :- ---- G~= 1 0-' J.l- ---- ... £= 10--3

[5

L1GO

10-

1 ~ l 0=0.1 -- ... ...

10~V~~~~~'~~~==~--=-=-:-~~ I /G~-1O-" : V V 0=0. 1 : aLiGO

10-11 '

l o--a 1 ~ 10'" 10-' I [Hz]

1

F igu re 8. ( From (I93J.) Spectra. of stochastic bockgrolluds from cosmic s~rings for lnrge loops (0. 1 the horizOIl size. solid llne;), for two values of the strillg tension Gillet spnnll ing a range of SCt'nl\rl08 motivated by brancworld inflation: lind for small loopli (with size 0 = 5fkGI" dnshtJd line), The cosmic-string sp,-..:truIII is distingu ishably diffcrtJllt from that of first-order phusc lrnll~itions 01' any other prediCl('(1 sonrce: it has Hearly COIII;tllnt energy ]J.er logarithillic frcquO':!I(':y iutel'ml over IIIlIlly dccIL<!es ILt high fr'-'1:IUenciea, I\nd falls olr lifter II l)Cak allow frequencies, since largc string loops arc rnre I\tld m.:!in te slowly. Cosmic strings may also produce dil;tinct ive bursts. produood by 1\ sharply bent bits of suing moving at nearly the speed of light [212, 213, 2 14 . 215].

is T., t.he redshifted frequency is

f:;::: 10- '] Hz H. x --:;::: 10 Hz --Imm - 4 (kuT.) c 1 ToV '

(3)

so the eLISA frequency bund t.'orresponds to t he horizon at and bcyond the Te7l1sco.le frontier of fu udameulill physies. T his allows eLISA to probe bulk motions at timcs about 3 x 10- 18_3 X 10- 10 s after the Dig Bang, a period not directly accessiblc with /lily other technique. Taking a typical broad spectrum into Hcconnt, eLISA has the sensiti vi ty to detc<:t cosmological backgrounds caused by new physics at el1crgies ...., O.J - JOOOTeV. if more than a (modest) fraction'" 10- 5 of the energy density is cOlln'rted to GWs at the timc of production.

Various sourct.'S of cos mo logical G \ V backgrounds nrc presented in dctail in (1931. Th<,y include first-order phase transitions, rcsulting in bubble nucleation and growth. and subsequcnt, bubble collisions aud t llrbulenCf' (19-1, 195. 196. 197, J9S]: t lu) dynumics of stabilhwtion for the extra dimensions required by sllpcrstri ug theory (199,200], which may also appeur as Ilon-Newtoll ian gravi ty in laboratory ex periml'nts at the sub-lIll11 scale: lletwol'ks of (:osmic (suPCI'-)strillgs !20 I. 202], which continuously produce loops that decay iuto G\\'s (sec F ig. 8); the tWllsitioll between inftlltioll and the hot Big Bung in the process of preheat ing !203. 20-1 . 205. 206. 207]: fiud the amplification of qU(t1uum vacuum RuctH8tions in some unco1l\'entional versions of iufbtion !208. 209. 210]. Alt hough the two-arm eLlSA dOl:'S not provide a Sagnac TDI cOl llbil1UliOll [211 ] to calibrate instrument 110i~ against posl;ible G\V backgrouuds. the clear spectral dependence predi<:ted for somc of theS() phenomena providcs <\n obser\'<ltiOl1al handle. as long ,15 the background lies abo\'(' the eLISA SCHsith'ity curve.

Low-/retJucTlcy gmvilaf1onal-wave science with eLISA/ NCO 16

As discussed in Sec. 4, obsenratiollS of GWs from ~lBH biuaries probe t he assembly of cosmic structures. In addition , binul'ies calL serve as standcml 8trens to measure cosmo logical parameters [216, 2171 b{,'Causc, 1.1.0; discussed arou nd Eq. (2), measuring the amplitude and fre<lucncy evolution of a binary sigl1111 yields t he absolute luminosity d ista nce to the source. Ho ..... 'Cver, binary G\Vs can not provide the source's rcdshift unless the other source parameters are known independently (because the rest mass of the binary is the only length/ time scale in the wa\'eform, the frequency evolution of a n .. xlshiftcd signal is indistinguishable from the signal from a heavier binary) . The optical redshift of the host galaxy can be obtained if an EM counterpart to ~lBH coalescence is obscrve<1 (sec, e.g. , [218 , 219, 2201, and [221j for a !'(x:c nt review).

" ' hile there arc many uncertuintit.'S in the nature and strength of such counterparts, sollie Inay be observable in t he local Universe. At z < 1, we expect that eLISA r-,·lBH-inspirul measurements could provide sky locations to better LhaH 400 deg2

for 50% of sources, and to 10 deg2 for 11%. (The incl usion of merger a nd ringdown in the analysil> should further improve these num~rs. ) Such large areas will be covered frequently and deeply by optical and radio surveys such as LSST [222] and the VAST project [223], identifying sufficiently distinctive transiellts. The accurate knowledge of the countcq >art't; rcdshift and position would then improve the uncertainty of GW-determin<:d parameters, with DL known to 1% for 60% of sources, and 5% for 87%. Such precise lumi nosity d istallce--redshift measurements wi\! be compiclllelltary to other coslilographieal cam paigns [224, 225], and will improve the estimation of cosmological panllllelers. Even wit hout counterpl.lrts, one may procee<l by cOllsidel'ing all possible hosts in a distance-position error box , and enforcing consistellcy betwccn multiple GW events [226]: t his should be possible for MBH binaries (and ElvlRIs [227]) in the local Universe, yielding the Hubble consta nt to a few percent.

8 . Conclusio ns

While LISA was always meant to be the definiti\'e mission in its frequency band , eLISA is being designed to provide the maximulII science within a cost cap. Neverthelt.'ss, as described above, eLISA will achie\'e a great purt of the LISA science gouls. It will represent the culmination of twenty years of excil ing, painstaking work, pioll{''Cring t.he new science of obscrvatiollallow-frcqucncy GW astronomy. rt will truly begin to unveil the hidden, distant Universe. ~rl:lY it Hy soon, ami safe.

Acknow ledglllcnts

This rcscarch was supported by the Dcutschcs Zclltrum mr Liift- lind Raumfahrt and by the 1rallsrcgio 7 ·'Gravitational Wav(.' Astronomy" financed by the Deutsche Forschungsgcltlcinschaft DFG (GertIHIIl Resell!'ch FOlllldat ion). EB was supported by :\'SF Grnllt PHY-0900735 and by KSF CAIU: ER Grant PHY-1055\03. AK was supported by the Swiss Kational Sdellee FOUlldatioll. TBL was support('d by:\'ASA Grant 08-ATFP08-012G. IlXL was Stlppol'tf'<1 by all appOilltJllcnt to the :\'ASA Postdoctoral Pl'ogl'lllll ti t the Goddard Space Flight Center. administered by Oak Ridge Associatt."'<1 Uui\'ersi ties t hl'Ough a cOlJtract \d th Z'ASA. ~ I V performed this work at the .Jet Propulsioll Laboratory. California Inst itute of Technology. under contract with the Xatiunal ACl'OlIam ies and Spa(,'C Administration. Copyright 2012.

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