(Ground-based) Gravitational wave astronomy

2

Gravitational waves exist!

•  Binary pulsars:

PSR B1913+16

Weisberg &!Taylor 03!

What are GW? Really: •  Required by Einstein’s gravity •  “Ripples” on spacetime •  Often highly nonlinear

This talk: •  Linear, spin-2 transverse wave •  Cause “length changes”: •  Like EM:

L

LLh Δ~

Example: Two black holes (no spin) Amplitude:

Two black holes Newtonian circular orbit

•  Characteristic relative length changes ~ (kinetic energy)/(distance)

€

h ~ 10−21 M /8M0( )5 / 3 d /30Mpc( )−1 f /100Hz( )2 / 3

r

d

3/~ rMΩ

( )π/22 Ω== orbff

( ) 3/22

2

2

~~1~ ΩMdM

dMv

dtId

dh

( ) ( ) 2/313 6/8/10 −−= MrMMHzf o

Sensitivity needed? (LIGO) ΔL ~ h L ~ 10-21 4km ~ 4 x 10-16 cm laser light ~ 10-4cm atom ~ 10-8cm

What makes GW?

Source: ~ any accelerating matter no screening Weak coupling: Imaging impractical:

(strong sources) <~ wavelength

•  Hard to make & detect •  Hard to obscure

Source: ~any accelerating charge screening limits size… s Strong coupling: Imaging often practical:

(common sources) >> wavelength

•  Easy to make & detect •  Easy to obscure

Gravitational Waves EM Waves

What makes GW?

Sources

f(Hz) λ(m)

10-8 1016

10-4 1012

10-2 1010

108

106

104

1

102

Detectors

Ground-based interferometers (LIGO/VIRGO/GEO/TAMA)

Big bang 10-6

Merging Black Holes: Big (center of galaxy) Small (post-supernova)

104

…and more!

Spinning neutron stars

Space-based interferometers (LISA)

Pulsar timing CMB fluctuations

LISA (planned) Detection I: Scale important

Detection II: How sensitive? Range: Depends (a) source (how much energy vs frequency) : dE/df (b) detector (preferred frequencies): Sh(f)

�4 �2 0 2

�22

�20

�18

�16

log f�Hz�

0.5logSh�1�Hz

�

100 200 300 400 500 600

1.0

10.0

5.0

2.0

20.0

3.0

30.0

1.5

15.0

7.0

f

d�Mpc

�

Dburst � c−1 1ρ

�2

5π2

∆Egw(G/c5)(f2Sh(f))

LISA (space) LIGO

(ground)

compare to flux threshold

D ��

L/4πFcrit

1052erg (=SN, all in GW)

What makes GW? Example: Two black holes (no spin) Waveform: 3 epochs

Inspiral: •  ~ Quasicircular orbits in potential V(r | L(t)) •  Amplitude by changing binding energy

Merger - Hard

Ringdown: - One perturbed hole “ringing”

Movie: black-holes.org

Binaries: Chirp •  Frequecy = 2*orbit…

•  Chirp: Frequency, amplitude increase –  Set by energy, energy loss rate

•  Identifying source: Where on the track are we? Chirp rate, not frequency at any time

Out[135]=

0 2 4 6 8 10

�3.�10�20

�2.�10�20

�1.�10�20

0

1.�10�20

2.�10�20

3.�10�20

Out[133]=

0 2 4 6 8 100

50

100

150

200

250

300

t

f�gw�

•  Sky location:

Wavelength set by detector: 100 Hz Detector d : 10 ms apart

Easier for bright sources (as 1/amplitude) Easier with complex sources (spin & polarization):

degeneracies

•  Mass Via chirp rate

df/dt -> mass [mass ratio : fine structure]

•  Distance

Absolute distance scale

€

SNR∝ M 5 / 6

d

Measurables: Inspiral

δθ � λ/d

Bonus material: Binary “track” h(f) “Amplitude” vs f: h(f): •  Key concept: “Track” h(f (t) ) for binaries •  Compare to detector sensitivities

D. Shoemaker, NSF review 2004

h(f)“ ∝ ”�

dE/df/f2

Bonus material: Supernova to BH Complex signal, several epochs [bounce; unstable NS; collapse; ringdown] Mostly high frequency (collapse time ~ R/c~ms), messy

Ott Dec 2010