The Scientific Potential of EMRI observations with NGO - APC

Thursday, 24 May 2012 

The Scientific Potential of 

EMRI observations with NGO 

Jonathan Gair (IoA, Cambridge) 

LISA Symposium, Paris, May 24th 2012


Talk Outline 

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

• Estimates of signal-to-noise ratios and event rates for EMRI 

detections using NGO and other potential configurations. 

• Parameter estimation accuracies for EMRIs. 

• EMRI science 

• Astrophysics - probe of massive black hole populations. 

• Cosmology - measurement of the Hubble constant. 

• Fundamental physics - test the “no-hair” property of 

black holes, test relativity.

Detector Configurations 

• Consider four different detector configurations 

- NGO: 1Gm arm length, 2 arms (4-link), 0.4m telescope, 2W 

laser power, DRS inertial sensor, 10 degree Earth-trailing orbit. 

- Classic LISA: 5Gm arm length, 20 degree Earth-trailing orbit. 

Consider both 3 arm (6-link) constellation and 2 arm (4-link) 

constellation. 

- 3-arm NGO: as NGO, but third arm restored (6 laser links). 

- 2Gm NGO: as NGO, but with 2Gm arm length. 

• Assume mission lifetime is 2 years in each case. 

Thursday, 24 May 2012

1/2 

Sh (f) 


1e-16 

1e-17 

1e-18 

1e-19 

NGO Sensitivity Curves 

Classic LISA 

1e-20 

0.0001 0.001 0.01 0.1 1 

f (Hz) 

NGO 

2 Gm NGO 

Classic LISA

EMRIs - SNRs 

• Characterise EMRI detectability 

in terms of the observable 

lifetime, tobs - the length of time 

during which LISA could start 

taking data and an event be 

observed with sufficient SNR. 

• Rate of observed events is then 

tobs/T, where T is the average time 

between plunges. 

• Compute observable lifetimes for 

EMRIs in the (e)LISA 

configurations using circular, 

equatorial Teukolsky fluxes. Take 

SNR detection threshold of 20. 


SNR accumulated 

60 

50 

40 

30 

20 

10 

0 

tlate 

tobs 

tearly 

0 5 10 15 20 25 

time remaining until plunge



• Contours of constant observable lifetime of 1 year, assuming all 

black holes are non-spinning and compact object mass m=10. 

z 

0 

0.2 

0.4 

0.6 

0.8 


3-arm NGO 


2-arm LISA 

1 

3-arm LISA 

10000 100000 1e+06 1e+07 

M


• Compute SNRs using analytic kludge waveforms to include 

eccentricity and as a cross-check. 

z 


0 

0.2 

0.4 

0.6 

0.8 NGO 



2-arm LISA 

3-arm LISA 

1 

10000 100000 1e+06 1e+07 

M 

Showing 

detection 

horizon 

for ep=0.25, 

a=0

EMRIs EMRIs - Parameter - Event Estimation Rates 

Configuration 

Black hole spin 

0 0.5 0.9 

NGO 45 50 90 

3-arm NGO 110 140 190 

2Gm NGO 150 165 250 

Classic LISA (2-arm) 600 650 750 

Classic LISA (3-arm) 1000 1150 1250 

• Note intrinsic rate uncertainties are an order of magnitude or more. 


EMRIs - Event Rates 

• BUT, have constraint on rate from total mass accreted by black 

holes. 

f 


100 

10 

1 

0.1 

0.01 

0.001 

10000 100000 1e+06 1e+07 

M (solar masses) 

m = 5 

m = 10 

m = 15 

m = 20

! EMRI (Gyr -1 ) 


1000 

100 

10 

1 

EMRIs - Event Rates 

f = 1 

f = 0.1 

f = 0.01 

0.1 

m = 5 

m = 10 

m = 15 

m = 20 

10000 100000 1e+06 1e+07 

M (solar masses)


• Assume all massive black holes have spin a=0.9 and detection with 

NGO. 

CO 

mass 

f = 0.01 f = 0.1 f = 1 

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

10 4 10 5 10 6 10 4 10 5 10 6 10 4 10 5 10 6 

5 7 7 4 20 20 5 30 25 5 

10 10 10 5 60 60 15 85 75 15 

15 15 15 10 90 90 30 160 150 30 

20 15 15 10 100 100 40 230 200 40 



• Consider dependence on black hole spin, assuming f = 0.1 and 

detection with NGO. 

CO 

mass 

a = 0 

Black Hole Spin 

a = 0.5 a = 0.9 


10 4 10 5 10 6 10 4 10 5 10 6 10 4 10 5 10 6 

5 5 5 0 10 10 < 1 20 20 5 

10 15 15 < 1 20 20 1 60 60 15 

15 15 15 < 1 30+1 30 5 90 90 30 

20 45 45 1 40+1 40 5 100 100 40 



• Consider dependence on detector configuration, assuming f = 0.1 

and compact object mass m = 10. 

Detector 

a = 0 

Black Hole Spin 

a = 0.5 a = 0.9 


10 4 10 5 10 6 10 4 10 5 10 6 10 4 10 5 10 6 

NGO 15 15 < 1 20 20 1 60 60 15 

3-arm 35+2 35 < 1 60+2 60 3 105+2 105 35 

2 Gm 50 45 2 60+2 60 5 140+3 140 45 

LISA 

( 2 arm) 

LISA 

( 3 arm) 


210 200 10 250 240 30 360 350 130 

340 300 20 370 340 50 490 460 160

dn/dlnM 

dn/dlnM 

0.5 

0.45 

0.4 

0.35 

0.3 

0.25 

0.2 

0.15 

0.1 

0.05 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 


EMRIs - Parameter - Event Properties Estimation 



2Gm NGO 

2-arm LISA 

3-arm LISA 

BH spin 

a = 0 

No mass 0 

Mass 

M 



fraction 

constraint 

2.5 

z 

Redshift 

0 

10000 100000 1e+06 1e+07 

0 

10000 100000 1e+06 1e+07 

M 


2-arm LISA 

3-arm LISA 

BH spin 

a = 0.9 

dn/dz 

dn/dz 

4.5 

4 

3.5 

3 

2.5 

2 

1.5 

1 

0.5 

2 

1.5 

1 

0.5 

0 




2-arm LISA 

3-arm LISA 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 

z 




2-arm LISA 

3-arm LISA

dn/dlnM 

dn/dlnM 

1 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

EMRIs - Parameter - Event Properties Estimation 




2-arm LISA 

3-arm LISA 

BH spin 

a = 0 

0 

f=0.1 mass 

Mass 

M 



fraction 

constraint 

2.5 

z 

Redshift 

0 

10000 100000 1e+06 1e+07 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 


0 

10000 100000 1e+06 1e+07 

M 


2-arm LISA 

3-arm LISA 

BH spin 

a = 0.9 

dn/dz 

dn/dz 

4.5 

4 

3.5 

3 

2.5 

2 

1.5 

1 

0.5 

2 

1.5 

1 

0.5 

0 




2-arm LISA 

3-arm LISA 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 

z 




2-arm LISA 

3-arm LISA

EMRIs - Parameter Estimation 

• Precision of EMRI parameter estimation is affected by 

configuration choice only through SNR. Parameter estimation 

accuracies for sources observed at a fixed SNR of 30 are very similar. 


Configuration 

Parameter NGO 3-arm NGO 2Gm NGO Classic LISA 

ln(M) 2x10 -4 2x10 -4 2x10 -4 2x10 -4 

ln(m) 1x10 -4 1x10 -4 1x10 -4 1x10 -4 

a 3x10 -4 3x10 -4 3x10 -4 3x10 -4 

Sky Pos. 2 o 1 o 2 o 1 o 

ln(D) 0.125 0.1 0.125 0.1

• A single EMRI event with an electromagnetic counterpart (and 

hence a redshift measurement) will give the Hubble constant to 

an accuracy of ~3%. N events give an accuracy of ~ 3/ %. 

√ N 


EMRI Science - Cosmology 

• Even without a counterpart, can estimate Hubble constant 

statistically (McLeod & Hogan 08) 

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





√ N 




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

McLeod & 

Hogan (2008)





√ N 





McLeod & 

Hogan (2008)




√ N 






- If ~20 EMRI events are detected at z < 0.5, will determine the 

Hubble constant to ~1%. 

• Analysis assumed typical distance uncertainties for Classic 

LISA. Pessimistically, 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.




√ N 






- If ~20 EMRI events are detected at z < 0.5, will determine the 

Hubble constant to ~1%. 

• Analysis assumed typical distance uncertainties for Classic 

LISA. Pessimistically, 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. 

• Any LISA-like detector will place constraints on H0.

EMRI Science - Fundamental Physics 

• Large number of waveform cycles generated in strong field make 

EMRIs ideal laboratories for fundamental physics 


- Verify ‘no-hair’ property of massive objects in centres of galaxies and 

hence test hypothesis that these are Kerr black holes. Hence test 

assumptions of the uniqueness theorem, i.e., axisymmetry, presence of 

a horizon, no closed-timelike-curves. 

- Look for signatures of astrophysical perturbations, e.g., accretion 

discs or other material in the black hole vicinity (Barausse et al., 

2007,2008) or massive perturbers (Yunes et al. 2011) etc. 

- Test theory of gravity, e.g., Brans-Dicke, dynamical Chern-Simons 

modified gravity (Sopuerta & Yunes 2009, Canizares et al. 2012). 

• These tests just rely on observing many EMRI waveform cycles. 

Any EMRIs detected can be used for fundamental 

physics tests.

Summary 

• Prospects for detection of EMRIs with NGO or a similar spacebased 

detector are good - expect tens of events at redshift z < 0.5. 

• EMRI parameter estimation precisions are comparable to 

estimates for Classic LISA for sources at a given SNR. 

• Strong potential for EMRI science - 

• Astrophysics - will obtain high precision measurements of black hole 

masses and spins; can beat current constraints on slope of black hole 

mass function with as few as ten observations. 

• Cosmology - measure Hubble constant to ~1-2% with ~20 events. 

• Fundamental physics - can use EMRI observations to test the black 

hole hypothesis and test relativity against alternative theories of gravity. 

• Descoped missions will offer the same range of science as Classic 

LISA, albeit with fewer events and reduced SNR for individual 

sources. However, large rate uncertainties arise from astrophysics.

The Scientific Potential of EMRI observations with NGO - APC

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