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 inspirals
• 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 104 M . M . 107 M ,
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.
EMRI event rates
•
Compute detection horizon assuming a threshold signal-to-noise
ratio of 20 is required for detection.
0.8
100
SNR
Redhsift z
0.6
0.4
0.2
0
4
AK
5
6
log10 (M• /M )
Teukolsky a• = 0
7
Teukolsky a• = 0.9
10
0
0.1 0.2
0.3
0.4
z
0.5
0.6
0.7
0.8
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, 104 M . M . 107 M
!
!
!
-
dN
= 0.002Mpc
d ln M
3
EMRI rate per galaxy has a simple power-law scaling with the
mass of the central black hole.
✓
◆ 0.17
M
1
R = 400Gyr
3 ⇥ 106 M
!
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.
EMRI event rates
•
CO
mass
Rate is somewhat dependent on assumptions about black hole spin
and compact object mass, but expect a few tens of events per year.
a=0
Black Hole Spin
a = 0.5
a = 0.9
No. events with M >
10
10
10
No. events with M >
10
10
10
No. events with M >
10
10
10
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
EMRI event properties
1
4.5
NGO
3-arm NGO
2Gm NGO
2-arm LISA
3-arm LISA
0.9
0.8
3.5
0.7
dn/dlnM
BH spin
a=0
0.5
0.4
dn/dz
3
0.6
2.5
2
1.5
0.3
1
0.2
0.5
0.1
0
10000
NGO
3-arm NGO
2Gm NGO
2-arm LISA
3-arm LISA
4
100000
1e+06
0
1e+07
0
0.1
0.2
0.3
0.4
M
0.9
0.8
Mass
0.6
0.7
0.8
0.9
1
0.9
1
z
Redshift
2.5
NGO
3-arm NGO
2Gm NGO
2-arm LISA
3-arm LISA
0.7
0.5
2
NGO
3-arm NGO
2Gm NGO
2-arm LISA
3-arm LISA
BH spin
a = 0.9
0.5
0.4
0.3
0.2
1.5
dn/dz
dn/dlnM
0.6
1
0.5
0.1
0
10000
100000
1e+06
M
1e+07
0
0
0.1
0.2
0.3
0.4
0.5
z
0.6
0.7
0.8
EMRI parameter estimation
•
•
0.6
0.6
0.4
0.4
0.2
0.2
0
–7
–6 –5 –4 –3 –2 –7 –6 –5 –4 –3 –2 –1
log( M/M), log( m/m)
log( a1)
Eccentricity at plunge
0
Quadrupole moment
0.6
0.6
0.4
0.4
0.2
0.2
0
pdf, a1
Spin (a1)
–7 –6 –5 –4 –3 –2 –6 –5 –4 –3 –2 –1
log( )
log( pl /epl )
0
0
pdf, Q
pdf, M, m
!
m2
⇠ 1 ⇥ 10 4
m2 of stellar remnants at the
at is the !mass distribution
actic centres and what is the role of mass segregation
!
relaxation in determining
a ⇠ 3the⇥nature
10 of4 the stellar
!
DLinhabiting
!
2
cores of ⌦
low⇠
mass
galaxies?
hole
5 deg
, Are they seed black
⇠ 10%
DL
!
Precision
arises
from
tracking
of galactic
nuclei, those
near the
horizons
of black
with masses
close
to the mass
the blackcycles.
hole at our
GW
phase
overof many
Not strongly dependent on
detector, at fixed signal-to-noise.
Redshifted mass (M, m)
pdf, e pl
EMRI observations provide very
precise
parameter
estimates!
ighly relativistic
orbit
around the massive
black hole
eld regions a few
m1
!
⇠ 2 ⇥ 10 4
m1
!
EMRI parameter estimation
•
These theoretical accuracy predictions have been confirmed in the
Mock
LISA Data
Report on
the second
Mock Challenges.
LISA Data Challenge
7
Table 3. Recovered SNRs and parameter errors for the EMRI signal in data
set 1.3.1. All errors are given as fractions of the allowed prior range for the
corresponding parameters (0.15 for e0 ), except for the errors on ν0 and D. Not
all parameters are shown. For their definitions, see tables 2 and 5 of [4]. The true
(optimal) SNR is 130.98.
SNR
BBGP 74.86
72.96
72.52
72.49
70.59
EtfAG
–
74.85
MT
76.52
δβ
δλ
δθK
δφK
δa
−0.33 −0.0095 −0.13 −0.076 0.28
−0.32
0.011 −0.15 −0.078 0.27
−0.28
0.025 −0.063 −0.036 0.41
−0.28
0.025 −0.063 −0.034 0.41
−0.31 −0.020 −0.36 −0.21
0.44
0.016 0.0012
–
– −0.082
0.15
0.47 −0.069 −0.15 −0.026
0.084 −0.49 −0.33 −0.10 −0.022
δµ
δM
−0.15
−0.15
−0.17
−0.17
−0.12
0.10
0.073
0.046
∆ν0
ν0
∆D
D
−0.51 0.017
0.21 −1.21
−0.51 0.017
0.21 −1.22
−0.35 −0.009
0.29 −2.15
−0.36 −0.009
0.29 −2.17
−0.12 −0.03
0.28 −0.91
−0.17 0.0026
0.098
–
0.18 0.00025 −0.11 −0.71
0.16 0.00026 −0.10 −0.70
MLDC round 2
4. Data sets 1.3.X: EMRIs
δe0
EMRI parameter estimation
•
These theoretical accuracy predictions have been confirmed in the
10
Mock LISA Data Challenges.
Mock LISA Data Challenges: from Challenge 1B to Challenge 3
Table 5. Overlaps and recovered SNRs for TDI observables A, E and combined
recovered SNR for data sets 1B.3.1–5.
Group
CA
BBGP
MT
1B.3.1 (SNRopt = 123.7)
0.57
51.0
0.58
0.998
86.1
0.997
51.6
88.3
72.5
123.4
BBGP
BBGPa
MT
1B.3.2 (SNRopt = 133.5)
0.07
6.6
0.18
0.39
37.6
0.41
0.54
49.5
0.54
18.2
39.8
50.8
17.6
54.7
70.9
1B.3.3 (SNRopt = 81.0)
−0.06
−4.2
−0.0003
−0.05
−0.2
−11.5 −0.32
−19.0
0.38
22.0
0.35
20.9
−3.0
−21.5
30.4
BBGP
BBGPa,c
MT
SNRA
CE
SNRE total SNR
BBGPb
1B.3.4 (SNRopt = 104.5)
0.0007
2.1
−0.0002
−0.8
0.16
13.9
0.04
6.7
2.1
14.6
BBGP
1B.3.5 (SNRopt = 57.6)
0.09
3.4
0.1
5.3
BBGPc
a
4.2
C and SNR after correcting the sign of β, lost on input to the MLDC webform.
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 likelihood
analytically over amplitude, which makes SNR sign-insensitive (a minus sign
corresponds to a change of π in the phase of the dominant harmonic). This
degeneracy is broken when all the harmonics are found correctly.
b
MLDC round 1B
EMRI parameter estimation
•
These theoretical accuracy predictions have been confirmed in the
Mock LISA Data Challenges.
Babak, JG & Porter (2009)
EMRI parameter estimation
•
These theoretical accuracy predictions have been confirmed in the
The Mock LISA
DataLISA
Challenges:
Challenge 3 to Challenge 4
7
Mock
Datafrom
Challenges.
Table 2. Parameter-estimation errors for the EMRIs in MLDC 3.3. M and µ are
the masses of the central and inspiraling bodies; ν0 and e are the initial azimuthal
orbital 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 spin
direction and sky position. SNRtrue is computed with the LISA Simulator; the
SNR 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
(SNRtrue )
SNR
∆M
M
−3
×10
∆µ
µ
−3
×10
∆ν0
ν0
−5
×10
∆λ
∆e0 ∆|S| λ SL ∆spin ∆sky
SL
×10−3 ×10−3 ×10−3 (deg) (deg)
∆D
D
EMRI-1 MTAPCIOA
(21.673) MTAPCIOA
21.794
5.05
3.29
21.804 −0.06 −0.01
1.61 −5.1 −1.4 −19
−0.08 −0.05
0.02
0.54
23
3.5
2.0
1.0
EMRI-2 MTAPCIOA
(32.935) BabakGair
BabakGair
BabakGair
32.387 −3.64 −2.61
22.790 33.1 −19.7
22.850 32.7 −20.0
22.801 33.5 −19.5
−3.09
3.8
10.1 −33
9.94 −32
10.5 −33
11
47
58
40
3.7 3×10−3
3.5 −0.25
3.5 −0.24
3.5 −0.25
EMRI-3 MTAPCIOA
(19.507) BabakGair
BabakGair
BabakGair
EtfAG
19.598
21.392
21.364
21.362
—
EMRI-4 MTAPCIOA
(26.650)
EMRI-5 MTAPCIOA
(36.173)
1.62
1.77
2.26
1.51
54.0
0.38
−0.10
1.01
1.95
1.88
2.71
1.01
2.09
4.88 −7375
−0.441 −8.77 −10.1
17.480 −3.32
5.00
−0.35
−1.2
−2.0
−1.3
26
−6.03 −3.7
−1.80
0.22
0.87 12
−7.3 250
−7.2 250
−7.4 240
−0.94
−0.68
−0.69
−0.50
17
−3.0
5.0
−2.3 116
−2.5 65
−1.7
7.6
—
—
144
950
99
55
62
43
0.07
0.13
3.0
4.5
6.1
6.2
32
−0.04
0.13
0.14
0.14
0.83
13
−2.3
1.8
−1.3
MLDC round 3
EMRI science: astrophysics
•
•
•
Large number of black
holes have been
observed, but mostly
high mass !
! M ⇠ 107 1010 M
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.
LISA
Plot from K Gultekin
Massive black holes: indirect constraints
•
Can infer mass function
indirectly via correlations.!
Use observed velocity
dispersions and M/
relation. Survey resolution
limited for M . 106 M .!
Use observed galaxy
luminosity function and
both L/ and M/
relations.!
Well-fit by the ansatz!
dn/d! log M = AM /(B + M ⇥ )
•
•
•
•
but slope at low-mass end
not well constrained.
Using EMRIs to probe the BH mass function
•
Parameterise the black hole mass function as a simple power-law!
!
dn/d log M = AM
•
Simplifying assumptions!
Consider measurements of M, z 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)!
!
R = 400Gyr 1 (M/3 ⇥ 106 M ) 0.17
Include parameter measurement errors in generation of data
only.!
Define detection horizon using an SNR cut of 20 as usual.
Using EMRIs to probe the BH mass function
0.2
14
12
10
8
6
4
2
0
0.15
α0
0.1
0.05
0
-0.05
-0.1
0
0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035
A0
Using EMRIs to probe the BH mass function
0.35
0.12
Optimistic LISA, no spin
Optimistic LISA, spin
Pessimistic LISA, no spin
Pessimistic LISA, spin
0.3
0.1
Optimistic LISA, no spin
Optimistic LISA, spin
Pessimistic LISA, no spin
Pessimistic LISA, spin
0.25
0)
0.2
(
(ln A0)
0.08
0.06
0.15
0.04
0.1
0.02
0.05
0
-0.3
-0.2
-0.1
0
0
0.1
0.2
0.3
0
-0.3
-0.2
-0.1
0
0
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.
0.1
0.2
0.3
Using EMRIs to probe the BH mass function
•
•
•
0.25
(ln A0)
0.2
0.15
0.1
0.05
0
0
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
N
0
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
N
0.1
0.09
0.08
0.07
0.06
0)
•
Most of the variation in
precision is explained by the
change in number of events.!
For pessimistic LISA,
no spin!
p
! (ln A0 ) ⇡ 0.8 10/Nobs
p
! (↵0 ) ⇡ 0.3 10/Nobs
For optimistic LISA, spin!
p
! (ln A0 ) ⇡ 0.5 10/Nobs
p
! (↵0 ) ⇡ 0.2 10/Nobs
eLISA has similar scaling!
p
! (ln A0 ) ⇡ 1.1 10/Nobs
! (↵ ) ⇡ 0.35p10/N
0
obs
but expect fewer events.
(
•
0.05
0.04
0.03
0.02
0.01
0
EMRI science: astrophysics
•
•
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: cosmography
•
•
•
Dimensionless gravitational wave strain scales as
M
(1 + z)M
h⇠
⇠
D
DL (z)
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.
EMRI science: cosmography
•
•
•
Dimensionless gravitational wave strain scales as
M
(1 + z)M
h⇠
⇠
D
DL (z)
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 &
(McLeod & Hogan 08)
-
Hogan (2008)
Let every galaxy in the LISA error box “vote” on the Hubble constant.
EMRI science: cosmography
•
•
•
Dimensionless gravitational wave strain scales as
M
(1 + z)M
h⇠
⇠
D
DL (z)
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 &
(McLeod & Hogan 08)
-
Hogan (2008)
Let every galaxy in the LISA error box “vote” on the Hubble constant.
EMRI science: cosmography
•
•
•
Dimensionless gravitational wave strain scales as
M
(1 + z)M
h⇠
⇠
D
DL (z)
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.
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•
Why should we test GR?
linear and dynamical gravity that is inaccessible to other probes.!
All GW sources
and detectors can be used to constrain fundamental
-1
10
LIGO NS-NS Merger
physics. ! -2
10
LIGO BH-BH
Merger
-3
Extreme-mass-ratio
inspirals are particularly good
because!
10
-4
Strong to
Field
Curvature
10
Long
duration
signals:
months
years in band; hundreds
of thousands of
IMRIs IMBH-SCO
-5
Strength cycles 10
for
typical EMRIs.! Tests
LISA IMBH-IMBH Merger
•
-1
[km ]
•
3 1/2
10
-7
1/2
Weak
Field
Tests
EMRIs SMBH-SCO
main sources Double
are black
hole binaries.!
Binary Pulsar
Figure from !
LISA SMBH-SMBH Merger N Yunes!
Rich dynamics:
expect
eccentricity
and
orbital
inclination for EMRIs.
-8
LAGEOS
adapted from!
10
Compact-9 object
explores
all
of
strong-field
space-time
as
it
inspirals.
D Psaltis!
Earth's Surface
10
Sun's Surface
Liv. Rev. Rel.!
-10
10
(2008)
ξ =(M/r )
-
-6
Clean 10
systems:
10
10
-11
Lunar Laser Ranging
-12
10
Perihelion Precession of Mercury
Field Strength
Pulsar Timing Arrays
-13
10
-12
10
-11
10
-10
10
-9
10
-8
10
-7
10
-6
10
ε=M/r
-5
10
-4
10
-3
10
-2
10
-1
10
0
EMRI science: fundamental physics
•
•
•
Gravitational wave observations probe a regime of strong-field, nonlinear 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.
Probing the nature and structure of BHs
•
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:
Ml + iSl = M (ia)l
Multipole moments are encoded in gravitational wave observables precession frequencies & number of cycles spent near a given
frequency (Ryan 95).
f2
2 dE/df
=f
∆N (f ) =
df /dt
dE/dt
Multipole moments enter at different orders in M Ω
!
"
4
2
S1
9 3 M2
Ωp
3
3 + ···
(M
Ω)
= 3(M Ω) − 4 2 (M Ω) +
−
Ω
M
2 2 M3
Also encoded in frequency and damping time of quasi-normal modes.
•
•
•
Probing BH structure: the central object
•
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%.
Barack & Cutler (2007)
Probing BH structure: the central object
•
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%.
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.
Probing BH structure: the central object
•
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%.
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)
Probing BH structure: the central object
•
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%.
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.
•
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).
Probing BH structure: influence of matter
•
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
•
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.
Barausse, Rezzolla, Petroff & Ansorg (2007)
Probing BH structure: influence of matter
•
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.
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.
Probing BH structure: influence of matter
•
Gravitational perturbations: material in Barausse
the vicinity&ofRezzolla
the MBH,(2008)
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.
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.
Probing BH structure: influence of matter
•
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.
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.
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)
6
Probing BH structure: influence of matter
•
Gravitational perturbations: material in the vicinity of the MBH,
10an accretion torus, could perturb the orbit (Barausse et al. 2007)
e.g.,
MM, !("h)
-
•
•
•
1
Orbits
in the same spacetime with and without a torus generate
significantly different GW signals.
0.1
GWs indistinguishable if black hole mass and spin also modified.
0.03
0.01
Inspiral should break this degeneracy.
-0.001
(17,45)
Hydrodynamic drag: if the orbit intersects matter (14,34)
in the spacetime
5
0.0001
(Barausse & Rezzolla 2008). Signature is a decreaseMin
orbital
=10
M., MM, Sys I
Sec
5
MSec=10 M., !("h), Sys I
inclination
during
inspiral.
1e-05
6
MSec=10 M., MM, Sys I
6 et al. 2012).
Migration
in
a
disc:
leads
to
~1
radian
dephasing
(Yunes
(11,24)
MSec=10 M., !("h), Sys I
1e-06
5
M
=10
M.,hole
MM, Sys
II
(8.5,19)
Massive perturbers: presence of a second massive Secblack
within
5
1e-07
MSec=10 M., !("h), Sys II
~0.1pc would leave
a detectable imprint. Second compact
object can
6
(5.8,12)
MSec=10 M., MM, Sys II
1e-08
6 et al. 2012)
(2.8,6)
lead to chaotic
motion in ~1% of EMRIs (Amaro-Seoane
MSec=10 M.,
!("h), Sys II
0
1
2
3
4
5
6
7
Yunes, Miller & Thornburg (2011) t [Months]
8
9
10
11
12
Probing BH structure: influence of matter
•
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.
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.
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)
Exotic matter: axion clouds (Arvanitaki & Dubovsky 2011); EMRI in
boson cloud dominated by boson accretion (Macedo et al. 2013).
EMRI science: fundamental physics
•
EMRI observations can also!
-
Constrain strong-field dynamics: Kerr orbits have a complete set of
-
Detect generic deviations from GR: use phenomenological models
-
integrals. Chaos (JG et al. 2008) or persistent resonances (Apostolatos et al.
2009) are qualitative indicators of non-Kerr spacetimes.
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 ChernSimons 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.