gravitational wave standard sirens as cosmological probes
DESCRIPTION
Gravitational wave standard sirens as cosmological probes. Neal Dalal (CITA) with D. Holz, S. Hughes, B. Jain. figure courtesy of AEI. Outline. overview of gravitational waves & detection GW’s from inspiraling binaries constraining cosmology. What are gravitational waves?. - PowerPoint PPT PresentationTRANSCRIPT
figure courtesy of AEI
Gravitational wave Gravitational wave standard sirens as standard sirens as
cosmological probescosmological probes
Neal Dalal (CITA)with D. Holz, S. Hughes, B. Jain
Outline
1. overview of gravitational waves & detection
2. GW’s from inspiraling binaries
3. constraining cosmology
What are gravitational waves?
Consider metric perturbation ga2(t) [+h].h is a symmetric 4£4 tensor, so 10 components:
• 4 scalar (spin 0) • 4 vortical (spin 1)• 2 shear (spin 2)
For ||h|| 1, linearized vacuum Einstein equations !
0)( 2
2
212
htc
so h satisfies a wave equation. The two spin-2 modes are transverse shear waves propagating at v=c.
What are gravitational waves?
think of GW’s as waves of tidal gravity.
change distance between free-falling observers
L ¼ L h(t)generated by moving masses, with amplitude
So need large m, v to be interesting!
intext22 ~~ 22
2
4 cv
rcGm
dtd
rcGh I
e.g. NS pair with v/c~0.3, observed at r 1000 km, has h~3¢10-4. So for a person of height 2m, L~1mm!
What are gravitational waves?
• essentially non-interacting with matter, once produced.
• act transverse to propagation direction.
• seem wimpy, but are dominant mechanism of energy loss for highly relativistic binaries!
Hulse-Taylor binary pulsarPSR 1913+16
GWologyGW generated by bulk motion of matter, unlike EM waves which are generated by many incoherent patches. GW are coherent, with a characteristic frequency of order the dynamical frequency, f / (G)1/2.
Therefore GW wavelength exceeds the size of the emitting region, ' R c/v. GW cannot resolve their sources and so cannot be used for imaging.
Also – important to remember that strain h is the observable, not the power. So the observable falls off like 1/r, not 1/r2 !
GWology
Schutz (1999)Schutz (1999)
ground vs. space-based
h 2L
L
Absence of a GW:Armlengths are arranged so that the light destructively interferes – no signal is measured.
How to detect?Laser interferometry!
Split laser beam, send light down long paths, with mirrors at each end. Bounce back,
recombine.
Presence of a GW:Positioning of mirrors changes, so armlengths change!Interference is no longer perfect, and we measure an output signal.
How to detect?Laser interferometry!
Split laser beam, send light down long paths, with mirrors at each end. Bounce back,
recombine.
The network of gravitational wave The network of gravitational wave detectorsdetectors
LIGO HanfordLIGO Hanford
LIGO LivingstonLIGO Livingston
ground based laser interferometersground based laser interferometersLIGO/VIRGO/GEO/TAMALIGO/VIRGO/GEO/TAMA
space-based laser interferometer (hopefully space-based laser interferometer (hopefully with get funded for a 201? Lauch)with get funded for a 201? Lauch)
LISALISA
ALLEGRO/NAUTILUS/AURIGA/…ALLEGRO/NAUTILUS/AURIGA/…resonant bar detectorsresonant bar detectors
ALLEGROALLEGROAURIGAAURIGA
Pulsar timing network, CMB anisotropyPulsar timing network, CMB anisotropy
The Crab nebula … a supernovae The Crab nebula … a supernovae remnant harboring a pulsar remnant harboring a pulsar
Segment of the CMB Segment of the CMB from WMAP from WMAP
Images from Patrick BradyImages from Patrick Brady
LIGO GW channel (as of ~ year ago) + injected waveform
Simulated waveform from a binary black hole merger (M1=M2 ~ 10 M๏, at ~ 15 Mpc)
Detection of the inspiral with a SNR~16 after application of the matched filtering algorithm
How do we observe sources?How do we observe sources?the gravitational wave strain is too small by the time the the gravitational wave strain is too small by the time the wave reaches earth to directly “see” the signalwave reaches earth to directly “see” the signal
How do we observe sources?How do we observe sources?
• For the majority of sources, some knowledge of the nature of the source is required for detection of a signal
• Matched filtering will be the primary tool for extracting small, quasi-periodic signals from the data stream
– But because many templates must be run, the SNR threshold for detection must be set high, typically SNR>8.5
• Techniques such as the excess power method can be used for other sources, or if less is known about the exact nature of the source
How well do we know the expected waveforms?
For some sources, well enough!For some sources, well enough!
Survey of some sourcesSurvey of some sourcesWaves from the early universe:
Initial state fluctuationsPhase transitionsCosmic strings
Rotating and vibrating compact objects:Rotating neutron starsModes of neutron star fluidModes of black holes (defer to binaries)
Binaries:Combinations of white dwarfs, neutron stars,and black holes.
Three phases of Three phases of coalescencecoalescence
figure from K. Thorne
1. Inspiral Members are widely separated, distinct bodies.
“Post-Newtonian” expansionworks well.
“Chirping” gravitational waveform
Post-Newtonian expansion• iterative approximation to fully dynamical spacetime
• expansion in (v/c)2.
• For 2-body problem, an accuracy of 3PN has been achieved by several independent methods; all approaches agree.[Blanchet, Damour, Esposito-Farèse, Iyer; Damour, Jarownowski, Schaefer; Itoh]
• reliable up to v/c ' 0.3-0.5
• expect orbits to be circularized quickly if GW emission is dominant energy loss
EC decomposition (in STT form) CTS decomposition (in Dirac coordinates)
•
•
•
•
•
•
•
•
slide from Samaya Nissanke
2. Merger Spacetime transition: From two distinct bodies to a single body.
NO expansion works well!
Modeling requires tackling full nastiness of nonlinear field equations, properties of stars.
Waveform unknown!
Image credit: Teviet Creighton, Caltech
Recent progress in numerical GR!
within past 1-2 yrs, several groups have successfully calculated mergers of comparable-mass BH’s!
lapse function in orbital plane
courtesy F. Pretorius
Recent progress in numerical GR!
within past 1-2 yrs, several groups have successfully calculated mergers of comparable-mass BH’s!
Newman-Penrose scalar 4 (like h+)
courtesy F. Pretorius
3. Ringdown If final state is a black hole, last waves come a system a distorted Kerr black hole.
Black hole perturbation theory describes thesystem.Waveform: Damped harmonic
oscillator.
Three phases of Three phases of coalescencecoalescence
figure from K. Thorne
only rely upon well-understood inspiral phase!
GW from inspirals• can get useful insight from quadrupole approximation
3/113/5
3/23/5
fMf
fD
Mh
Chirp
L
Chirp
• if we observe how fast the frequency chirps, we know how much energy is being radiated in GW. By comparing to the measured strain amplitude, this tells us how distant the source is!(Schutz 1986)
GW from inspirals• the phase evolution is just determined by time until coalescence, tct, and by a combination of masses called the (redshifted) chirp mass
5121
5321
)(
)(chirp )1(
mm
mmzM
• the strain amplitude also depends on same combination!
)](cos[)angles()(
)(3235
chirp tD
tfMth
L
F
• but – emission is not isotropic: depends on inclination • can measure inclination if polarization is measured!
• measured amplitude depends on source direction • can measure this from timing of received signals
GW standard sirens
so the gravitational radiation from inspiraling binaries provides a self-calibrating distance indicator. Just need detectors with different locations and different orientations, to measure polarization and timing.
LIGO Hanford
LIGO Livingston
can achieve this with a network of detectors on Earth …
… while LISA can do both in space!
Cosmology with standard sirens
GW observatories can measure precise distances to sources at cosmological distances.
can be useful for cosmology!H2(z)=8G/3 [m(z)+(z)+K(z)+…]
and dL(z)=(1+z)s (c/H) dz
One problem: distances but no redshifts!So we need merger events that have some sort of EM counterpart to use them as standard sirens.
Binary neutron stars
• known to exist and radiate in GW.
• Galactic merger rate about 10-4 yr-1.
• very plausible that merger could have optical / X-ray counterpart, esp. if it produces BH with accretion disk.
movie courtesy M. Shibata
are short GRBs from NS coalescence??
Short GRBs• origin of short GRBs is still unknown, but NS mergers are a leading candidate!
•if NS merger ! GRB, they are ideal
•afterglow/host galaxy gives z
•known direction decreases distance errors
•known time reduces required SNR threshold!
Cosmology with GW from GRBs
• assume 4-element network of detectors (LIGO-H, LIGO-L, Virgo, AIGO) of comparable sensitivity
• double NS merger detectable out to 600 Mpc.
• distance errors improveif sources are collimated
• GRB trigger may not be necessary! Can get minutesto hrs warning from GW, ~degree localization, good enough for follow-up?
20± beaming
unbeamed
Cosmology with GW from GRBs
unbeamed100 GRBs
unbeamed
20± beaming
How well does this constrain cosmological parameters e.g. dark energy equation of state parameter w?
But how is this possible? We’re using GRBs only out to 600 Mpc, z . 0.15. How can or w be constrained?
Absolute distances!• this works because GW measure absolute distances to sources, in Mpc, not h-1 Mpc. The CMB tells us distance to LSS also in Mpc, so combining the two can measure DE parameters!
• put another way: for flat universe, only 3 parameters: {h, m, w}. CMB provides 2 constraints, on m h2, and on lA= dA(LSS)/rs. A 3rd constraint, like a measurement of H0, determines all three.
• works for any H0 determination, e.g. using water masers. Measuring H0 = measuring w !
more precisely, measures integral constraint on w(z), assuming flat universe.
other GW sources
• focused on GRBs since they have afterglows and a (reasonably) known rate from BATSE, Swift.
• other stellar mass inspirals in LIGO bands, like NS-BH, BH-BH, could also serve as standard sirens, if they have EM counterparts.
• if -rays beamed, but afterglows less so, then even off-axis GRBs could be useful!
• what about LISA?
source frequency (Hz)source frequency (Hz)
sou
rce
sou
rce
“str
en
gth
”“s
tren
gth
”
1010441010-12-12 1010-8-8 1010-4-4 11
relics from the big bang, inflationrelics from the big bang, inflation
exotic physics in the early universe: phase transitions, cosmic strings, domain walls, …exotic physics in the early universe: phase transitions, cosmic strings, domain walls, …
1-10 M1-10 M๏๏ BH/BH BH/BH
mergersmergers
NS/BH mergersNS/BH mergers
NS/NS mergersNS/NS mergers
pulsars, pulsars, supernovaesupernovae
EMR inspiralEMR inspiral
NS binariesNS binaries
WD binariesWD binaries
101022-10-1066 M M๏๏ BH/BH BH/BH
mergersmergers
>10>1066 M M๏๏ BH/BH mergersBH/BH mergers
CMB CMB anisotropyanisotropy
Pulsar timingPulsar timing LISALISA LIGO/…LIGO/…Bar Bar detectordetectorss
Overview of expected gravitational wave Overview of expected gravitational wave sourcessources
Binary black holes in the UniverseBinary black holes in the Universe• Strong circumstantial evidence that black
holes are ubiquitous objects in the universe
– supermassive black holes (106 M๏ - 109 M๏) thought to exist at centers of most galaxies
• high stellar velocities near the centers of galaxies, jets in active galactic nuclei, x-ray emission, …
– more massive stars are expected to form BH’s at the end of their lives
VLA image of the galaxy NGC 326, with HST image of jets inset. CREDIT: NRAO/AUI, STScI (inset)
• Galaxy mergers are observed commonly, suggesting SMBH mergers may also be common.
• LISA can detect all SMBH mergers within the horizon (e.g out to z=10) !
Two merging galaxies in Abell 400. Credits: X-ray, NASA/CXC/ AIfA/D.Hudson & T.Reiprich et al.; Radio: NRAO/VLA/NRL)
Cosmology with LISA
• for LISA standard sirens to be useful, must have ~100 to average out lensing
• merger rates, EM counterparts still uncertain!
100 GW sources, 0<z<2
Conclusions!
• exciting times for GW astronomy• waveforms from inspirals of compact
object binaries are well-understood• these provide a self-calibrating
distance indicator• the number of sources detectable
with ground-based detectors is large enough to provide interesting constraints on cosmology!
upcoming experiments
LIGO • operating at target sensitivity• began science run Nov 2005, expect to continue through 2007• 2008, begin upgrade to LIGO-II (10£ increase in sensitivity!)• LIGO-II begins operations around 2009
Virgo• European observatory, similar sensitivity, expect to follow LIGO by 2-3 yrs
AIGO• Australian observatory, funding uncertain
LISA: ???
slide from Keith Riles
LIGO-IICollaboration between LIGO and GEO600, to upgrade to advanced sensitivity (10£ increase).
• increased laser power (10W ! 100W) • new test mass material (sapphire), lower internal thermal noise in bandwidth• increased test mass (10kg ! 40kg)• new suspension: single ! quadruple pendulum• improved seismic isolation (passive ! active)
10£ increase in sensitivity gives 1000£ in volume!
LISA
LISA - The Overview Mission Description
– 3 spacecraft in Earth-trailing solar orbit separated by 5 x106 km.
– Gravitational waves are detected by measuring changes in distance between fiducial masses in each spacecraft using laser interferometry
– Partnership between NASA and ESA
– Launch date ~2015+
Observational Targets
– Mergers of massive black holes
– Inspiral of stellar-mass compact objects into massive black holes
– Gravitational radiation from thousands of compact binary systems in our galaxy
– Possible gravitational radiation from the early universe
LISA
Orbits
Three spacecraft in triangular formation; separated by 5 million km
Spacecraft have constant solar illumination
Formation trails Earth by 20°; approximately constant arm-lengths
1 AU = 1.5x108 km
LISA
Determining Source Directions
Directions (to about 1 degree) : 2 methods: AM & FM
FM: Frequency modulation due to LISA orbital doppler shifts
– Analagous to pulsar timing over 1 year to get positions
– FM gives best resolution for f > 1 mHz
AM: Amplitude modulation due to change in orientation of array with respect to source over the LISA orbit
– AM gives best resolution for f < 1 mHz
Summary: LISA will have degree level angular resolution for many sources (sub-degree resolution for strong, high-frequency sources)
– See e.g. Cutler (98), Cutler and Vecchio (98), Moore and Hellings (00), also Hughes (02)
(Cornish and Larson, ’01)(F+ & Fx)
LISA
Determining Source Distances
Distances(to about 1%) Binary systems with orbital evolution (df/dt)
– “Chirping” sources
– Determine the luminosity distance to the system by comparing amplitude, h, and period derivative, df/dt, of the gravitational wave emission
– Quadrupole approximation:
Luminosity distance (DL) can be estimated directly from the detected waveform
See e.g. work by Hughes, Vecchio for quantitative estimates
3/113/5
3/23/5
fMf
fD
Mh
Chirp
L
Chirp
LISA
Determining Polarization
LISA has 3 arms and thus can measure both polarizations
Gram-Schmidt orthogonalization of combinations that eliminate laser frequency noise yield polarization modes
– Paper by Prince et al. (2002)
– gr-qc/0209039
L2 L3
L1
(notation from Cutler,Phinney)
X
Y
hHHL
LLL
hHHL
LL
YXXY
YYXX
2
3
4
3)2(
2
3
4
3)(
132
13
LISA
LISA Sensitivity
2-arm “Michelson” sensitivity +White Dwarf binary background
2-arm “Michelson” sensitivity
frequency0.1 mHz 1 Hz
Acceleration Noise(Disturbance Level)
h Tobs
Shot Noise (Measurement Sensitivity)
Short- Limit
White Dwarf Background
(Includes gravitational wave transfer function averaged over sky position and polarization). Source sensitivities plotted as hSqrt(Tobs).
LISA
Rate Estimates for Massive Black Hole Mergers
[Sesana et al, astro-ph/0401543]
Use hierarchical merger trees Rate estimates depend on
several factors– In particular space density of
MBHs with MBH<106 M
– Depends on assumptions of formation of MBHs in lower mass structures at high-z
Some recent estimates– Sesana et al. (2004): about 1 per
month
– Menou (2003): few to hundreds per year depending on assumptions
– Haehnelt (2003): 0.1 to 100 per year depending on assumptions
3 year mission
courtesy T. Prince
LISA
Can LISA Detect Massive Black Holes Mergers?
courtesy T. Prince
Is there an optical counterpart?
• Some modeling suggests likely counterpart
e.g. delayed afterglow (Milosavljevic & Phinney 2004) • inspiral hollows out circumbinary gas• subsequent infall after merger
MacFadyen & Milosavljevic (2006)
• Much more work is warranted
• Regardless of what theorists have to say, error box will be scrutinized for counterparts
Distance determination with optical counterpart
• Typical luminosity distance to much better than 1%
Ultimate standard candle!
Holz & Hughes (2005)
Cosmology with LISA standard sirens
• Non-evolving equation-of-state: / a -3(1+w)
3,000 SNe, 0.7<z<1.7
2 GWs, z=1.5, z=3.
3,000 SNe + 2 GWs
Tremendously powerful probe of dark energy
BEWARE
Gravitational lensing
• The Universe is mostly vacuum, with occasional areas of high density– Photons do not experience a
Robertson-Walker Universe• Gravitational lensing due to
matter inhomogeneities causes a change in brightness of observed images– strong lensing: tremendous
increase in brightness, and multiple images
– weak lensing: slight increase or decrease in brightness
Gravitational Lensing• uniform, isotropic Robertson-Walker universe is
generally assumed– Key assumption: the Universe is filled with
homogeneous matter
Gravitational LensingMagnification Distributions
Probability distribution, P(), of magnification, , due to gravitational lensing
The average magnification is given by the Robertson-Walker value (normalized to 1)
The distributions are peaked at <1, with tails to high magnification
Every source at high z has been gravitationally lensed
z=1
Cosmology with SMBH standard sirens
Without the effects of gravitational lensing
3,000 SNe, 0.7<z<1.7
3,000 SNe + 2 GWs
When neglecting lensing, even a few SMBH standard sirens have a major impact on cosmology!
Cosmology with SMBH standard sirens
Including the effects of gravitational lensing
3,000 SNe, 0.7<z<1.7
3,000 SNe + 2 GWs
3,000 SNe + 2 GWs + lensing
Lensing seriously compromises the use ofSMBH standard sirens!