Overview of science with extreme-mass-ratio inspirals€¦ · white dwarf, neutron star or black hole) into a SMBH. ! • Main sequence stars tidally disrupted so do not form EMRIs.!

Overview of science with extreme-mass-ratio inspirals

Jonathan Gair, Cambridge (IoA)!Xth LISA Symposium, Gainesville, May 20th 2014

Talk Outline

• Brief introduction to extreme-mass-ratio inspirals (EMRIs)!

• Expected EMRI event rates for eLISA!

• Parameter estimation accuracies!

• Science with extreme-mass-ratio inspiral observations!

- Astrophysics!

- Cosmology!

- Fundamental physics

• Extreme mass ratio inspiral (EMRI): inspiral of a compact object (a white dwarf, neutron star or black hole) into a SMBH. !

• Main sequence stars tidally disrupted so do not form EMRIs.!

• Originate in dense stellar clusters through direct capture, binary splitting, tidal stripping of giant stars or star formation in a disc.!

• For black holes with mass in the range , EMRIs will generate gravitational waves detectable by eLISA.!

• Standard picture: EMRIs begin with capture of a compact object on a very eccentric orbit by the central black hole. !

• Complex gravitational waveforms include three fundamental frequencies - orbital frequency, perihelion precession frequency and orbital plane precession frequency.

104M . M . 107M

Extreme-mass-ratio inspirals

EMRI event rates

• Compute detection horizon assuming a threshold signal-to-noise ratio of 20 is required for detection.

4 5 6 7

log

10

(M•/M)AK Teukolsky a• = 0 Teukolsky a• = 0.9

0

0.2

0.4

0.6

0.8

Redhsiftz

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

z

10

100

SN

R

Teukolsky a• = 0.9

EMRI event rates

• Estimate number and properties of eLISA events by assuming!

- Mass function of black holes is flat in logarithm in the LISA range,

!

!

- EMRI rate per galaxy has a simple power-law scaling with the mass of the central black hole.

!

!

- EMRI orbits are circular and equatorial, so we can use Teukolsky results. Assume all black holes have the same spin, a = 0, 0.5, 0.9.

104M . M . 107M

dN

d lnM= 0.002Mpc3

R = 400Gyr1

M

3 106M

0.17

EMRI event rates

• Rate is somewhat dependent on assumptions about black hole spin and compact object mass, but expect a few tens of events per year.

Black Hole Spina = 0 a = 0.5 a = 0.9

CO mass

No. events with M > No. events with M > No. events with M >10 10 10 10 10 10 10 10 10

5 5 5 0 10 10 < 1 20 20 510 15 15 < 1 20 20 1 60 60 1515 15 15 < 1 30+1 30 5 90 90 3020 45 45 1 40+1 40 5 100 100 40

EMRI event properties

BH spin a = 0

BH spin a = 0.9

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

10000 100000 1e+06 1e+07

dn/d

lnM

M

NGO3-arm NGO2Gm NGO

2-arm LISA3-arm LISA

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10000 100000 1e+06 1e+07

dn/d

lnM

M

NGO3-arm NGO2Gm NGO


0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

dn/d

z

z

NGO3-arm NGO2Gm NGO


0

0.5

1

1.5

2

2.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

dn/d

z

z

NGO3-arm NGO2Gm NGO


Mass Redshift

EMRI parameter estimation

• EMRI observations provide very precise parameter estimates!

!!!!!!!!

• Precision arises from tracking GW phase over many cycles. Not strongly dependent on detector, at fixed signal-to-noise.

5 deg2,DL

DL 10%

in a highly relativistic orbit around the massive black hole eld regions a few

-

-

What is the mass distribution of stellar remnants at the galactic centres and what is the role of mass segregation and relaxation in determining the nature of the stellar

inhabiting the cores of low mass galaxies? Are they seed black hole

-gions of galactic nuclei, those near the horizons of black holes with masses close to the mass of the black hole at our –7 –6 –5 –4 –2–3

log(©a1)

pdf,

a1

Redshifted mass (M, m) Spin (a1)

pdf,

M, m

log(©M/M), log(©m/m)

pdf,

Q

pdf,

e

Eccentricity at plunge Quadrupole moment

log(©E /e )pl pl log(©1)

–7

–6

–6 –5 –4 –2–3 –1–7 –6 –5 –4 –2–30

0.2

0.4

0.6

0

0.2

0.4

0.6

0

0.2

0.4

0.6

0

0.2

0.4

0.6

0–5 –4 –2–3 –1

pl

a 3 104

m1

m1 2 104

m2

m2 1 104


• These theoretical accuracy predictions have been confirmed in the Mock LISA Data Challenges.Report on the second Mock LISA Data Challenge 7

Table 3. Recovered SNRs and parameter errors for the EMRI signal in dataset 1.3.1. All errors are given as fractions of the allowed prior range for thecorresponding parameters (0.15 for e0), except for the errors on ν0 and D. Notall parameters are shown. For their definitions, see tables 2 and 5 of [4]. The true(optimal) SNR is 130.98.

SNR δβ δλ δθK δφK δa δµ δM ∆ν0

ν0δe0

∆DD

BBGP 74.86 −0.33 −0.0095 −0.13 −0.076 0.28 −0.15 −0.51 0.017 0.21 −1.2172.96 −0.32 0.011 −0.15 −0.078 0.27 −0.15 −0.51 0.017 0.21 −1.2272.52 −0.28 0.025 −0.063 −0.036 0.41 −0.17 −0.35 −0.009 0.29 −2.1572.49 −0.28 0.025 −0.063 −0.034 0.41 −0.17 −0.36 −0.009 0.29 −2.1770.59 −0.31 −0.020 −0.36 −0.21 0.44 −0.12 −0.12 −0.03 0.28 −0.91

EtfAG – 0.016 0.0012 – – −0.082 0.10 −0.17 0.0026 0.098 –

MT 74.85 0.15 0.47 −0.069 −0.15 −0.026 0.073 0.18 0.00025 −0.11 −0.7176.52 0.084 −0.49 −0.33 −0.10 −0.022 0.046 0.16 0.00026 −0.10 −0.70

4. Data sets 1.3.X: EMRIs

Three groups reported parameter sets for the EMRIs in data sets 1.3.1–1.3.4. Nogroup tackled the problem of detecting these systems in data set 2.2 (on top of theGalactic background).

BBGP Babak and colleagues used an MCMC matched-filtering search that modeledthe signal with a sequence of progressively longer templates (a time-annealedscheme).

EtfAG Gair, Mandel and Wen used a TF track search that (for now) targeted onlythe intrinsic parameters and sky position [10].

MT Cornish used an MHMC matched-filtering search, running it in parallel onindividual month-long segments, which were subsequently strung together forfull detections.

Table 3 shows typical recovered SNRs and errors. While it is clear that the matched-filtering searches locked on several secondary probability maxima with comparableprobabilities, the recovered SNRs correspond to solid detections with exceedingly lowfalse-alarm probabilities. The errors are quoted as fractions of the allowed parameterranges, and they are quite large. Intriguingly, the TF search was the most accuratein determining the sky position. Altogether, these challenges demonstrated a positivecapability of detecting EMRIs, at least if their signals are similar in complexity tothe kludge waveforms used in this challenge [4]; however, the prospects for accurateparameter estimation are still uncertain, and a good focus for further challenges.

5. Conclusion

We are very excited about the outcome of the first two MLDCs, which have givena convincing demonstration that a significant portion of the LISA science objectivescould already be achieved with techniques that are currently in hand. Most of theresearch groups that participated in Challenge 1 have successfully made the transitionto the greater complexity of Challenge 2. Challenge 3 will continue to move in thedirection of more realistic signals, featuring chirping Galactic binaries and precessing

MLDC round 2


• These theoretical accuracy predictions have been confirmed in the Mock LISA Data Challenges.The Mock LISA Data Challenges: from Challenge 1B to Challenge 3 10

Table 5. Overlaps and recovered SNRs for TDI observables A, E and combinedrecovered SNR for data sets 1B.3.1–5.

Group CA SNRA CE SNRE total SNR

1B.3.1 (SNRopt = 123.7)

BBGP 0.57 51.0 0.58 51.6 72.5MT 0.998 86.1 0.997 88.3 123.4

1B.3.2 (SNRopt = 133.5)

BBGP 0.07 6.6 0.18 18.2 17.6BBGPa 0.39 37.6 0.41 39.8 54.7MT 0.54 49.5 0.54 50.8 70.9

1B.3.3 (SNRopt = 81.0)

BBGP −0.06 −4.2 −0.0003 −0.05 −3.0BBGPa,c −0.2 −11.5 −0.32 −19.0 −21.5MT 0.38 22.0 0.35 20.9 30.4

1B.3.4 (SNRopt = 104.5)

BBGPc 0.0007 2.1 −0.0002 −0.8 2.1BBGPb 0.16 13.9 0.04 6.7 14.6

1B.3.5 (SNRopt = 57.6)

BBGP 0.09 3.4 0.1 4.2 5.3

a C and SNR after correcting the sign of β, lost on input to the MLDC webform.b C and SNR after correcting phases at t = 0, to account for a BBGP bug.c The BBGP SNRs can be negative because BBGP maximized likelihoodanalytically over amplitude, which makes SNR sign-insensitive (a minus signcorresponds to a change of π in the phase of the dominant harmonic). Thisdegeneracy is broken when all the harmonics are found correctly.

• Data set 3.1 contains a Galactic GW foreground from ∼ 60 million compactbinary systems. This data set is a direct descendant of Challenge 2.1, but itimproves on the realism of the latter by including both detached and interactingbinaries with intrinsic frequency drifts (either positive or negative). Section 3.1gives details about the binary waveform models, about their implementation inthe LISAtools suite [16], and about the generation of the Galactic population.

• Data set 3.2 contains GW signals from 4–6 binaries of spinning MBHs, on top ofa confusion Galactic-binary background. This data set improves on the realismof Challenges 1.2.1–2 and 2.2 by modeling the orbital precession (and ensuingGW modulations) due to spin–orbit and spin–spin interactions. Section 3.2 givesdetails about the MBH-binary waveforms.Because this challenge focuses on the effects of spins rather than on the jointsearch for MBH signals and for the brightest Galactic binaries, the backgroundis already partially subtracted—it is generated from the population of detachedbinaries used for Challenge 3.1, withholding all signals with SNR > 5.

• Data set 3.3 contains five GW signals from EMRIs. As in Challenges 1.3.1–

the conversion to Synthetic LISA’s dimensionless fractional frequency fluctuations is described on[19, p. 6]; the values actually used in the MLDCs are

Sacc(f) = 2.5 × 10−48(f/Hz)−2[1 + (10−4 Hz/f)2] Hz−1;

Sopt(f) = 1.8 × 10−37(f/Hz)2 Hz−1.

MLDC round 1B


• These theoretical accuracy predictions have been confirmed in the Mock LISA Data Challenges.

Babak, JG & Porter (2009)


• These theoretical accuracy predictions have been confirmed in the Mock LISA Data Challenges.The Mock LISA Data Challenges: from Challenge 3 to Challenge 4 7

Table 2. Parameter-estimation errors for the EMRIs in MLDC 3.3. M and µ arethe masses of the central and inspiraling bodies; ν0 and e are the initial azimuthalorbital frequency and eccentricity; |S| is the dimensionless central-body spin; λSL

is the spin–orbit misalignment angle, and D the luminosity distance. ∆spin and∆sky are the geodesic angular distances between the estimated and true spindirection and sky position. SNRtrue is computed with the LISA Simulator; theSNR for each entry with the simulator used in that search (the LISA Simulator[26] for MTAPCIOA, Synthetic LISA [27] for EtfAG and BabakGair).

Source Group SNR ∆MM

∆µµ

∆ν0ν0

∆e0 ∆|S|∆λSLλSL

∆spin ∆sky ∆DD

(SNRtrue) ×10−3 ×10−3 ×10−5 ×10−3 ×10−3 ×10−3 (deg) (deg)

EMRI-1 MTAPCIOA 21.794 5.05 3.29 1.61 −5.1 −1.4 −19 23 2.0 0.07(21.673) MTAPCIOA 21.804 −0.06 −0.01 −0.08 −0.05 0.02 0.54 3.5 1.0 0.13

EMRI-2 MTAPCIOA 32.387 −3.64 −2.61 −3.09 3.8 0.87 12 11 3.7 3×10−3

(32.935) BabakGair 22.790 33.1 −19.7 10.1 −33 −7.3 250 47 3.5 −0.25BabakGair 22.850 32.7 −20.0 9.94 −32 −7.2 250 58 3.5 −0.24BabakGair 22.801 33.5 −19.5 10.5 −33 −7.4 240 40 3.5 −0.25

EMRI-3 MTAPCIOA 19.598 1.62 0.38 −0.10 −0.35 −0.94 −3.0 5.0 3.0 −0.04(19.507) BabakGair 21.392 1.77 1.01 1.95 −1.2 −0.68 −2.3 116 4.5 0.13

BabakGair 21.364 2.26 1.88 2.71 −2.0 −0.69 −2.5 65 6.1 0.14BabakGair 21.362 1.51 1.01 2.09 −1.3 −0.50 −1.7 7.6 6.2 0.14EtfAG — 54.0 4.88 −7375 26 17 — — 32 0.83

EMRI-4 MTAPCIOA −0.441 −8.77 −10.1 −6.03 −3.7 144 950 99 13 −2.3(26.650)

EMRI-5 MTAPCIOA 17.480 −3.32 5.00 −1.80 0.22 55 62 43 1.8 −1.3(36.173)

errors in spin magnitude and orientation were significantly larger than for othersources, and the distance to both sources was overestimated by factors of 2 or 3(vs. errors ! 10% for the other EMRIs). Furthermore, the negative SNR for claimedEMRI-4 and the low FFs between the recovered and injected noiseless waveformsindicate that the MTAPCIOA search could not resolve these sources individually, butconverged on two parameter sets that jointly fit the combination of the two injectedsources.

5. Cosmic-string–cusp bursts (MLDC 3.4)

Challenge dataset 3.4 contained three burst signals from cosmic-string cusps, immersedin instrument noise with slightly randomized levels for each individual noise (i.e., fromthe six proof masses and photodetectors). The dataset was less than a month long (221

s), with a higher sampling rate (1 s) than the others, to accommodate the potentialhigh-frequency content of these signals, which have power-law spectrum up to an fmax

determined by the characteristic length scale of the string and the viewing angle (see[7] for more details about the waveforms and the random choice of their parameters).Four collaborations submitted entries:

• CAM (a collaboration between Cambridge U. and APC–Paris) used MultiNest.

• CaNoe (researchers at Cambridge and Northwestern Universities) implementeda time–frequency algorithm, a modified version of CATS [22].

• JPLCIT (Caltech/JPL) experimented with MCMC and MultiNest, but onlysubmitted entries based on the latter [28].

• MTGWAG (Montana State University) used a parallel-tempering MCMC [25].

MLDC round 3

EMRI science: astrophysics

• Large number of black holes have been observed, but mostly high mass !

!• Only a handful of black

holes known with mass estimates in the LISA/eLISA range.!

• Models of structure growth are tuned to reproduce high mass end of mass function, but give varying predictions at low mass end.

Plot from K Gultekin

LISA

M 107 1010M

Massive black holes: indirect constraints

• Can infer mass function indirectly via correlations.!

• Use observed velocity dispersions and relation. Survey resolution limited for .!

• Use observed galaxy luminosity function and both and relations.!

• Well-fit by the ansatz!

!• but slope at low-mass end

not well constrained.

M/

M/L/

dn/d log M = AM/(B + M)

M . 106M

Using EMRIs to probe the BH mass function

• Parameterise the black hole mass function as a simple power-law!

!

• Simplifying assumptions!

- Consider measurements of only. !

- EMRIs are circular and equatorial.!

- All black holes have spin a=0 or 0.9.!

- EMRI rate per black hole has known mass scaling (Hopman 09)!

!- Include parameter measurement errors in generation of data

only.!

- Define detection horizon using an SNR cut of 20 as usual.

dn/d log M = AM

M, z

R = 400Gyr1(M/3 106M)0.17


0 2 4 6 8 10 12 14

A0

α0

0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035-0.1

-0.05

0

0.05

0.1

0.15

0.2


0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

(ln

A0)

0

Optimistic LISA, no spinOptimistic LISA, spin

Pessimistic LISA, no spinPessimistic LISA, spin

0

0.02

0.04

0.06

0.08

0.1

0.12

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

(

0)

0

Optimistic LISA, no spinOptimistic LISA, spin

Pessimistic LISA, no spinPessimistic LISA, spin

Effect of varying assumptions about LISA and BH spin.! “Pessimistic LISA’’ - 2 year mission, 1 data channel.! “Optimistic LISA” - 5 year mission, 2 data channels.! “Spin” - all black holes have a=0.9.! “No spin” - all black holes have a=0.


• Most of the variation in precision is explained by the change in number of events.!

• For pessimistic LISA, no spin!

!!

• For optimistic LISA, spin!

!!

• eLISA has similar scaling!

!!

• but expect fewer events.

0

0.05

0.1

0.15

0.2

0.25

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

(ln

A0)

N

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000

(

0)

N

(lnA0

) 0.8p

10/Nobs

(lnA0

) 0.5p

10/Nobs

(↵0

) 0.3p

10/Nobs

(↵0

) 0.2p

10/Nobs

(lnA0

) 1.1p

10/Nobs

(↵0

) 0.35p

10/Nobs

• Have assumed scaling of EMRI rate with BH mass is known. Might break this degeneracy by combining EMRI and SMBH observations.!

• EMRI observations will also tell us about!

- Black hole spin distribution!

- EMRI formation mechanisms ‣ Capture: eccentric and inclined orbits.!

‣ Binary splitting: circular, inclined orbits.!

‣ Formation of compact objects in a disc: circular, equatorial orbits.!

‣ Tidal-stripping of massive stars: circular, inclined orbits and low mass compact objects.!

- Stellar populations in dense stellar clusters ‣ EMRI rates probe dynamical processes, e.g., relaxation.!

‣ Masses probe stellar IMF and mass segregation.

EMRI science: astrophysics

h MD (1 + z)MDL(z)

EMRI science: cosmography

• Dimensionless gravitational wave strain scales as

• Can use this to probe cosmological parameters (Schutz 1986) if the mass/redshift degeneracy can be broken: electromagnetic counterparts or apply statistical methods to multiple observations.

• Use LISA observations of EMRIs to measure the Hubble constant (McLeod & Hogan 08)

- Let every galaxy in the LISA error box “vote” on the Hubble constant.

h MD (1 + z)MDL(z)






McLeod & Hogan (2008)

h MD (1 + z)MDL(z)






McLeod & Hogan (2008)

h MD (1 + z)MDL(z)






- If ~20 EMRI events are detected at z < 0.5, LISA would determine the Hubble constant to ~1%.

• eLISA could have a factor 2 larger distance error; ~20 events at z < 0.5 would provide ~2% Hubble measurement, ~80 events would provide 1% precision. We expect to see a few tens of EMRIs with eLISA, all at z < 0.5.

EMRI science: fundamental physics

• Gravitational wave observations probe a regime of strong-field, non-linear and dynamical gravity that is inaccessible to other probes.!

• All GW sources and detectors can be used to constrain fundamental physics. !

• Extreme-mass-ratio inspirals are particularly good because!

- Long duration signals: months to years in band; hundreds of thousands of cycles for typical EMRIs.!

- Clean systems: main sources are black hole binaries.!

- Rich dynamics: expect eccentricity and orbital inclination for EMRIs. Compact object explores all of strong-field space-time as it inspirals.

GW Tests of GR Yunes

10-12 10-11 10-10 10-9 10-8 10-7 10-6 10-5 10-4 10-3 10-2 10-1 100

ε=M/r10-1310-1210-1110-1010-910-810-710-610-510-410-310-210-1

ξ1/2 =(

M/r3 )1/

2 [km

-1]

Double Binary Pulsar

Lunar Laser Ranging

LIGO BH-BH Merger

Sun's SurfaceEarth's Surface

LISA IMBH-IMBH Merger

Perihelion Precession of Mercury

LIGO NS-NS Merger

IMRIs IMBH-SCO

LAGEOSLISA SMBH-SMBH Merger

EMRIs SMBH-SCO

Pulsar Timing Arrays Field Strength

Curvature Strength

GWs can probe the non-linear, dynamical, strong-field regime

Strong Field Tests

Weak Field Tests

Will, Liv. Rev., 2005, Psaltis, Liv. Rev., 2008, Siemens & Yunes, Liv. Rev. 2013.

Why should we test GR?

Figure from !N Yunes!adapted from!D Psaltis!Liv. Rev. Rel.!(2008)


• Gravitational wave observations probe a regime of strong-field, non-linear and dynamical gravity that is inaccessible to other probes.!

• All GW sources and detectors can be used to constrain fundamental physics. !

• Extreme-mass-ratio inspirals are particularly good because!

- Long duration signals: months to years in band; hundreds of thousands of cycles for typical EMRIs.!

- Clean systems: main sources are black hole binaries.!

- Rich dynamics: expect eccentricity and orbital inclination for EMRIs. Compact object explores all of strong-field space-time as it inspirals.

• GW emission from EMRIs encodes a map of the space-time structure outside the central massive black hole.

• Can characterize a vacuum, axisymmetric spacetime in GR by its multipole moments. For a Kerr black hole, these satisfy the ‘no-hair’ theorem:

• Multipole moments are encoded in gravitational wave observables - precession frequencies & number of cycles spent near a given frequency (Ryan 95).

• Multipole moments enter at different orders in

• Also encoded in frequency and damping time of quasi-normal modes.

Ml + iSl = M(ia)l

∆N (f) =f2

df/dt= f2

dE/df

dE/dtMΩ

Ωp

Ω= 3(MΩ)

2

3− 4

S1

M2(MΩ) +

(

9

2−

3

2

M2

M3

)

(MΩ)4

3 + · · ·

Probing the nature and structure of BHs

• Need infinite number of multipoles to describe Kerr. Instead, consider “bumpy” black holes with small departures from Kerr.

- Many studies, e.g., Collins & Hughes (2004), Glampedakis & Babak (2005), Barack & Cutler (2007), JG, Li & Mandel (2008), Sopuerta & Yunes (2009), Canizares, JG & Sopuerta (2012).

- Can simultaneously measure M, a to ~0.01% and excess quadrupole to ~0.1%.

Probing BH structure: the central object

Barack & Cutler (2007)




• Information about the surface of the central object is also encoded in emitted GWs

• Horizon: presence/absence of a horizon indicated by cut-off/continuation of emission at plunge, e.g., persistent emission for an inspiral into a Boson-Star.








Kesden, Gair & Kamionkowski (2004)






• Tidal coupling: Energy is lost ‘into the horizon’ through tidal heating. Infer tidal interaction by comparing observed energy flux to observed inspiral rate (Li & Lovelace 07).

• Quasi-normal mode structure: QNMs of non-Kerr black holes can also be distinct, e.g., ‘grava-star’ (Pani et al. 2009).


• Gravitational perturbations: material in the vicinity of the MBH, e.g., an accretion torus, could perturb the orbit (Barausse et al. 2007)

- Orbits in the same spacetime with and without a torus generate significantly different GW signals.

- GWs indistinguishable if black hole mass and spin also modified.

Probing BH structure: influence of matter




Barausse, Rezzolla, Petroff & Ansorg (2007)Barausse, Rezzolla, Petroff & Ansorg (2007)





- Inspiral should break this degeneracy.

• Hydrodynamic drag: if the orbit intersects matter in the spacetime (Barausse & Rezzolla 2008). Signature is a decrease in orbital inclination during inspiral.







Barausse & Rezzolla (2008)







• Migration in a disc: leads to ~1 radian dephasing (Yunes et al. 2012).

• Massive perturbers: presence of a second massive black hole within ~0.1pc would leave a detectable imprint. Second compact object can lead to chaotic motion in ~1% of EMRIs (Amaro-Seoane et al. 2012)









Probing BH structure: influence of matter 6

of signal A is

ρ(A) =√

(A| A) , (17)

while the overlap between signals a and b is

M = max(A| B)

√

(A| A) (B| B). (18)

with the mismatch MM = 1 − M. The max label inEq. (18) is to remind us that this statistic must be maxi-mized over an event time (e.g., the time of coalescence ofthe EMRI system) and a phase shift [26]. If the overlapis larger than 97% (or equivalently, if the mismatch islower than 3%), then the difference between waveformsA and B is sufficiently small to not matter for detectionpurposes (see e. g. [40]). The minimum overlap quotedabove (97%) is mostly conventional, motivated by thefact that the event rate scales as the cube of the overlapfor a reasonable source distribution. For an overlap largerthan 97%, no more than 10% of events are expected tobe lost at SNRs of O(10). Of course, for larger SNRs,one might not need such high overlaps, although EMRIsources are expected to have SNRs < 100.Whether the difference between waveforms A and B

can be detected in parameter estimation can be assessedby computing the SNR of the difference in the waveformsδh ≡ A−B:

ρ(δh) =√

(δh| δh) = 4Re

∫ ∞

0

δh(f) δh⋆(f)

Sn(f)df . (19)

When this SNR equals unity, then one can claim that Aand B are sufficiently dissimilar that they can be differ-entiated via matched filtering (see e. g. [41]).We applied these measures to EOB waveforms with

and without acceleration of the COM. The results areplotted in Fig. 4 as a function of observation time inmonths. The vertical dotted lines correspond to obser-vation times of (0.5, 2, 4, 6, 9, 12) months, and the num-bers next to them, in parenthesis, stand for the SNRof Sys. I and II for that observation time. The differ-ent line styles and colors correspond to mismatches andSNRs of the error for different secondary systems. Ob-serve that the mismatch is always smaller than 0.03 (thesolid black horizontal line), suggesting that this effectwill not affect detection. Observe also that the SNR ofthe difference reaches unity (the dashed black horizontalline) in between 6 and 12 months of observation, and forthe MSec = 106 M⊙, ρ(δh) reaches ∼ 10 after one year.This suggests that given a sufficiently strong EMRI withSNR ∼ 50− 100, the magnitude of this effect is in prin-ciple detectable within one year of coherent integration.

V. DEGENERACIES

Now that we have determined that there exists a setof plausible perturber parameters for which the magni-

0 1 2 3 4 5 6 7 8 9 10 11 12t [Months]

1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.010.03

0.1

1

10

MM

, !("

h)

(2.8,6)(5.8,12)

(11,24)

(14,34)(17,45)

(8.5,19)

MSec=105M., MM, Sys I MSec=105M., !("h), Sys IMSec=106M., MM, Sys I MSec=106M., !("h), Sys IMSec=105M., MM, Sys IIMSec=105M., !("h), Sys IIMSec=106M., MM, Sys IIMSec=106M., !("h), Sys II

FIG. 4. Mismatch as a function of time in units of monthsfor Sys. I and II and different perturber masses, all at a sep-aration of rSec = 0.1 pc. SNRs for Sys. I and II are given inparentheses for a source at 1 Gpc.

tude of the correction could be measurable, let us con-sider the possibility of degeneracies. That is, let us in-vestigate whether we can mimic an acceleration of theCOM by changing the intrinsic parameters (the com-ponent masses, the spin parameter, etc.) in the non-accelerating waveform. The simplest way to see whetherthis is possible is to study the frequency dependence ofthe GW modification introduced by the COM’s acceler-ation.Let us then remind ourselves of how the frequency-

domain representation is constructed. For this, we em-ploy the stationary-phase approximation (see e. g. [42]),under which, the frequency-domain waveform is simply

h(f) = Af−7/6eiψ(f) , (20)

where the Newtonian (leading-order) amplitude is A =π−2/330−1/2 M5/6D−1

L , with M = η3/5M , while thephase is constructed from

ψ(f) = −π

4+ 2πft(f)− 2φ(f) , (21)

where the second term arises due to the Fourier transformand the third term due to the oscillatory nature of thetime-domain waveform.The phase of the frequency-domain waveform in the

stationary phase approximation is then controlled bythese last two terms in Eq. (21). The first term can becomputed via

2πft(f) = 2πf

∫ f/2 τ(F ′)

F ′dF ′ , (22)

where f is the GW frequency, while the second term canbe calculated from

φ(f) = 2π

∫ f/2

τ(F ′)dF ′ , (23)

Yunes, Miller & Thornburg (2011)








• Exotic matter: axion clouds (Arvanitaki & Dubovsky 2011); EMRI in boson cloud dominated by boson accretion (Macedo et al. 2013).



• EMRI observations can also!

- Constrain strong-field dynamics: Kerr orbits have a complete set of integrals. Chaos (JG et al. 2008) or persistent resonances (Apostolatos et al. 2009) are qualitative indicators of non-Kerr spacetimes.

- Detect generic deviations from GR: use phenomenological models to constrain arbitrary deviations (Yunes & Pretorius 2009; JG & Yunes 2012).

- Test GW polarisation: eLISA has sensitivity to the four additional polarisations permissible in metric theories (Tinto, da Silva Alves 2010).

- Test quadrupole formula: compare observed inspiral rate to quadrupole formula prediction to detect excess energy loss, e.g., dipole radiation in Brans-Dicke (Scharre & Will 2002)

- Constrain alternative theories of gravity: test scalar-tensor gravity (Scharre & Will 2002; Berti, Buonanno & Will 2005), dynamical Chern-Simons modified gravity (Canizares et al. 2012), scalar Gauss-Bonnet gravity (Yagi 2012).

Summary

• eLISA should observe a few tens of EMRI events per year.!

• For each event, eLISA will track the waveform phase for hundreds of thousands of orbits.!

• Allows parameter measurements to unprecedented precision.!

• EMRIs have fantastic scientific potential for!

- Astrophysics ‣ phenomenology of massive black holes at low redshift.!

‣ stellar populations and dynamics in dense stellar clusters.!

- Cosmology ‣ measure Hubble constant to ~1%.

- Fundamental physics ‣ spacetime structure outside astrophysical black holes.!

‣ tests of gravitational physics and theory of relativity.

Documents

Overview of science with extreme-mass-ratio inspirals€¦ · white dwarf, neutron star or black hole) into a SMBH. ! • Main sequence stars tidally disrupted so do not form EMRIs.!