astrophysics to be learned from observations of intermediate mass black hole in-spiral events...

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


Outline

• Some jargon and fundamental scales• Sensitivity• Astronomy with laser interferometers • Information extraction: astrophysics and cosmology• Conclusions


Observational window

Advanced resonant

107 105 103

10 Msun


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]


Sensitivity (low redshift)

Merger: Flanagan and Hughes parameters (optimistic!); Ring-down: a/m = 0.98

Advanced LIGO

LISA

In-spiral

Whole coalescence


Optimal filtering is assumed

Sensitivity (low redshift)

Merger: Flanagan and Hughes parameters (optimistic!); Ring-down: a/m = 0.98


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


• 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


(Cutler, 1998;

Tinto et al, 2000)

Signal at detector output

Chirp mass and distance

Physical parameters: masses and spins


Wave cyclesNewt. 1PN tail spin-orbit

2PN spin-spin

Penn State, 20th – 22nd May 2004 A Vecchio

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


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


Simple precession

L

(Apostolatos et at, 94; Kidder, 95)

J = L + S

S = S1 + S2

-N



Sky location

Location, orientation

and

spins and masses


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


(AV astro-ph/0304051)

Low redshift IMBHs (cont’d)


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


High redshift IMBHs


High redshift IMBHs (cont’d)


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


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)


IMBH + SMBH

(Finn and Thorne, 2000)[D = 1 Gpc; circular orbit and spinning SMBH]


IMBH + SMBH (cont’d)

[D = 1 Gpc; eccentric orbit and non-spinning SMBH]

(Barack and Cutler, gr-qc/0310125)


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


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


astrophysics to be learned from observations of intermediate mass black hole in-spiral events...

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