Astrophysics to be learned from observations of
intermediate mass black hole in-spiral events
Alberto Vecchio
Making Waves with Intermediate Mass Black Holes
PennState, 20th – 22nd May 2004
Three classes of sources
• IMBH – BH(IMBH)• IMBH – IMBH• SMBH – IMBH
PennState, 20th – 22nd May 2004 A Vecchio
Some questions
• Do IMBHs exist?• Demographics of IMBHs:
– Masses – Spins– ….
• Mass vs redshift distribution– Hierarchical clustering– Structure formation
• IMBHs and their environment• Dynamical processes in clusters• BH and SMBHs studies
PennState, 20th – 22nd May 2004 A Vecchio
Outline
• Some jargon and fundamental scales• Sensitivity• Astronomy with laser interferometers • Information extraction: astrophysics and cosmology• Conclusions
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Observational window
Advanced resonant
107 105 103
10 Msun
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Coalescence of binary systems
f = 4 [ M (1+z) /103 M ]-1 Hz f = 32 [ M (1+z) /103 M ]
-1 Hz
Long lived Short lived
[Kip’s cartoon]
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Sensitivity (low redshift)
Merger: Flanagan and Hughes parameters (optimistic!); Ring-down: a/m = 0.98
Advanced LIGO
LISA
In-spiral
Whole coalescence
PennState, 20th – 22nd May 2004 A Vecchio
Optimal filtering is assumed
Sensitivity (low redshift)
Merger: Flanagan and Hughes parameters (optimistic!); Ring-down: a/m = 0.98
PennState, 20th – 22nd May 2004 A Vecchio
Optimal filtering is assumed
Whole coalescence
LIGO-I
Sensitivity (high redshift)
z = 30
z = 5
z = 0.5
m1 = m2
z = 0.5
z = 5
z = 30
m2 = 0.01 m1
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• ESA/NASA joint mission (launch: 2012)
• ESA cornerstone mission
• NASA “Beyond Einstein Initiative” mission with ConX
• Space-borne laser interferometers with 5 million km arms, 30 cm diameter telescopes and 1 W lasers
• Powerful GW telescope: thousands of signals at anyone time
• LISA Pathfinder: technology demonstrator
Binary systems
L
m2 m1D_L
S2 S1
N
Penn State, 20th – 22nd May 2004 A Vecchio
The most general system is described by 17 parameters:
Masses [2] and spins [6]
Orbit [4]
Sky position and distance [3]
Arbitrary initial time and phese [2]
Michelson observables
i = II
i = I
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(Cutler, 1998;
Tinto et al, 2000)
Signal at detector output
Chirp mass and distance
Physical parameters: masses and spins
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Wave cyclesNewt. 1PN tail spin-orbit
2PN spin-spin
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Signal at detector output
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LISA: the orbit
LISA motion• Two key (and distinct) motions:
1. LISA orbits the Sun: the signal frequency is Doppler shifted
2. Spacecraft constellation rotates around the normal to the detector plane: the response of the detector is not fixed, that is the antenna pattern is time dependent
• The signal is therefore phase and amplitude modulated
• The LISA motion is essentially what provides the detector pointing capability
PennState, 20th – 22nd May 2004 A Vecchio
Frequency/ Hz
Δf
Δf ~ 2/TLISA ~ 7 × 10-8 Hz
Δf ~fGW (vLISA/c) ~ 10-7 (fGW /1 mHz) Hz
orientationmotio
n
~1 mHz
Induced frequency shifts
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Simple precession
L
(Apostolatos et at, 94; Kidder, 95)
J = L + S
S = S1 + S2
-N
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Signal at detector output
Sky location
Location, orientation
and
spins and masses
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Signal modulationsm1 = 107 Msun
m2 = 105 Msun
SdotL = 0.5
S/m2 = 0.95
m1 = 106 Msun
m2 = 106 Msun
SdotL = 0.9
S/m2 = 0.3
PennState, 20th – 22nd May 2004 A Vecchio
(AV astro-ph/0304051)
Low redshift IMBHs (cont’d)
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Low redshift IMBHs (cont’d)
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Low redshift IMBHs (cont’d)
• Confirm existence of IMBH• Demographics and properties• Identify time of possible EM burst due to collision for
follow-on observations but error box larger than 1 sq. degree– Studies of IMBHs and their environment are not likely
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High redshift IMBHs
PennState, 20th – 22nd May 2004 A Vecchio
High redshift IMBHs (cont’d)
PennState, 20th – 22nd May 2004 A Vecchio
High redshift IMBHs (cont’d)
• Confirm existence of IMBH at high redshift• Demographics and properties• Distance known to ~1%-30%
– Redshift can (in principle) be reconstructed with a fractional error ~ 10%-20% (or better, as errors on cosmological parameters decrease; Hughes, 2002)
– However, weak lensing will degrade our ability of reconstructing D(z) (Markovic, 1993; Holz and Hughes, 2003)
• Concrete chance of studying structure formation
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Some caveats
• Circular orbits • Only leading quadrupole included in the amplitude: other
harmonics can refine information extraction (Sintes and AV, 2000; Hellings and Moore, 2001)
• For radiation at f > 5 mHz, LISA transfer function behaviour (not taken into account here) will improve parameter estimation, angular resolution in particular (Seto, 2003; AV and Wickham, 2004)
• Estimate of the errors are based on Cramer-Rao bound, which is a tight lower bound for high SNR (Finn, 1992; Dhurandhar et al, 1998; Nicholson and AV, 1998)
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IMBH + SMBH
(Finn and Thorne, 2000)[D = 1 Gpc; circular orbit and spinning SMBH]
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IMBH + SMBH (cont’d)
[D = 1 Gpc; eccentric orbit and non-spinning SMBH]
(Barack and Cutler, gr-qc/0310125)
PennState, 20th – 22nd May 2004 A Vecchio
IMBH + SMBH (cont’d)
[D = 1 Gpc; eccentric orbit and non-spinning SMBH]
(Barack and Cutler, gr-qc/0310125)
PennState, 20th – 22nd May 2004 A Vecchio
IMBH + SMBH (cont’d)
[D = 1 Gpc; eccentric orbit and non-spinning SMBH]
(Barack and Cutler, gr-qc/0310125)
PennState, 20th – 22nd May 2004 A Vecchio
IMBH + SMBH (cont’d)
• For binary systems at D ~ 1 Gpc:– IMBH and SMBH mass with fractional error < 1
part in 10,000– Distance with fractional error < 10%– Location of the source in the sky within an error
box < 0.001 srad – Spin of SMBH better than 10-4
PennState, 20th – 22nd May 2004 A Vecchio
Conclusions
• GW observations: confirmation of existence of IMBH• Mass vs z(D) distribution of IMBH • Demographics of IMBH • IMBH can also provide a census of SMBHs up to z ~
a few and possibly close-by BHs• (Advanced) LIGO has a fighting chance of detecting
IMBHs and measuring at least the mass
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