1. Sources of Gravitational Waves: an Overview
Bernard Schutz
Albert Einstein Institute
Potsdam, Germany

2. Gravitational Wave Physics
GW observations will require a mix of five key ingredients:
good detector technology
good waveform predictions
good data analysis methodology and technology
coincident observations in several independent detectors
coincident observations in electromagnetic astronomy
Source studies aim at 2. and 5., and at understanding what information is likely to come from observations. They underpin 3. Source studies require input from GR and from astrophysics.
Waveform predictions: the nonlinearity of GR makes detailed computation of sources difficult. But nonlinearity is an essential part of the problem, since almost all sources are driven to radiate by self-gravitation. (Exception: GW pulsars.)
Astrophysics input helps focus effort on the most interesting and/or promising sources: theory/modeling & data-analysis effort.
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

3. Astrogravs: Overview of GW Sources
Tools of the trade
The two-body problem has been studied with 2 methods:
post-Newtonian methods (weak-field/low-velocity)
radiation-reaction methods (restricted 2-body problem, one mass very small).
The one-body problem (isolated NS/BH oscillations) can be studied with perturbation approximations.
“Cosmic modesty” of BHs seems to allow study even of dynamical BH pairs by the close-limit approximation.
Outside these regimes, and for most other sources, numerical simulation studies are our only hope.
To guide astrophysical estimates, where waveform predictions are not required, quasi-Newtonian order-of-magnitude formulas are useful.
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

4. Gravitational Waves in a Quasi-Newtonian Nutshell
Generation:
Upper limit:
internal potential
Newtonian potential
Energy Flux:
all classical field theories
dimensional factor
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

5. Astrogravs: Overview of GW Sources
Polarization
Gravitational waves have 2 independent polarizations, illustrated here by the motions of free “test” particles.
They follow the motions of the source TT-projected on the sky.
Interferometers are linearly polarized detectors.
A measurement of the degree of circular polarization determines the inclination of a simple binary orbit. If the orbit is more complex, as for strong spin-spin coupling, then the changes in polarization tell what is happening to the orbit.
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

6. Gravitational Dynamics/
Frequency
Luminosity
very strong dependence
on compactness /
Timescale
Chirp time  is a measure of light-
crossing time
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

7. Detectors Measure Distances: Chirping Binaries are Standard Candles
If a detector measures not only f and h but also  for a binary, then it can determine its distance r.
For a circular binary, upper bounds are attained, so:
Combining this with f itself gives us M and R, and then the value of h gives us r, the distance (luminosity distance ).
If a chirping massive black-hole binary is identified so that a redshift can be obtained, then one can do cosmology: H0, q0. LISA can measure f, , and h to 0.1% accuracy.
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

8. GW physics across the spectrum
2 x 100 M BHs coalesce in 1 yr from ~ 0.1 Hz
A chirping system is a GW
standard candle: if position is known, distance can be inferred.
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

9. Kicks and Binary Lifetimes
Pure quadrupole radiation carries no net linear momentum. To get a kick you need quadrupole-octupole coupling, whose flux is down by a factor of v/c from quadrupole.
The momentum flux P is the energy flux c, so the total radiated momentum (allowing for angular factors) is at most 0.2 Lv/c2. Assuming that this happens in the last half orbit (Pmin/2) leads to a recoil velocity no larger than
Holes must come within a separation Rmax to coalesce in a Hubble time, where
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

10. Taxonomy of GW Waveforms1 3 5 4 6 2
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

11. Chirping and coalescing binaries
LIGO I/GEO/VIRGO could see BH CBs to 100 Mpc, may be first detected source
Adv LIGO should see many BH CBs per year to z~0.5
Range very dependent on masses and on modeling of late-stage waveform
Adv LIGO should see similar numbers of NS coalescences out to ~500 Mpc.
No NS-BH binaries in Galactic pulsar population yet
LISA will see SMBH coalescences M everywhere, also M coalescences to z~1.
LISA will see chirping WD, NS binaries in Galaxy, predict future coalescences, measure distances
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

12. Black-Hole Coalescences
Waveform:
Early inspiral well-understood using pN methods, getting even better.
Transition, plunge, merger still needs work.
Possible first source for LIGO I/GEO/VIRGO, confidence difficult!
Most spectacular source for LISA, huge S/N
Event rates for LIGO, LISA very uncertain 
Population: 
Data analysis: 
Potential for the unexpected: 
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

13. Issue: BH Merger Simulations
Improving all the time:
More stable forms of the field equations
Gauge conditions improved
Run times lengthening
Initial data must be improved: subtle
Boundary conditions not yet satisfactory
EU- funded network “Sources of Gravitational Waves” pushing all of these issues.
Still hungry for computer time. The Discovery Channel funded AEI’s longest simulation to date, and its visualization. (Seidel, Benger, et al, AEI)
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

14. Black-Hole Simulations: Next Steps
Still very far from having reliable waveforms
Adaptive, dynamical mesh refinement needed to give good resolution with long run times
Stability of codes still an issue past 50 M
Run time an issue: Lazarus
Outer boundary condition a critical issue
Initial data exploration essential, unequal masses too
Is the plunge sudden or gradual?
EU network has applied for (an will probably get) renewal/extension. Will soon be a NASA-NSF initiative to stimulate work here. In my view the field needs several complementary collaborations.
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

15. Black Hole Binary Populations
Manufactured in globular clusters, more work needed on GC evolution, early GC population, …
SMBH binaries: many uncertainties --
Growth of SMBHs (by merging of smaller holes or by accretion?)
Timescale for galaxy mergers to produce BH mergers
Relation of binary pairs and recent mergers to galactic activity
Very active area of research (this conference!)
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

16. Astrogravs: Overview of GW Sources
Data analysis for CBs
Construction of search templates for NS-NS binaries well understood, most S/N from inspiral
More massive systems shift to lower frequency, so for LIGO the S/N becomes more dependent on the plunge-merger phase. Don’t yet know how best to do these searches.
LISA: SMBH coalescence will be visible without filtering, but good fitting needed to remove signals without contaminating weaker signals also present. Not clear if this will be possible for merger phase (a few minutes for each event).
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

17. Gravitational Capture by SMBH
Recent strong progress on self-interaction problem (restricted two-body problem) in GR. Accurate orbit calculations in near future.
Complexity of waveform family poorly understood, work needed on hierarchical methods.
Confusion with more distant sources possible, especially if population is large.
Great interest in testing GR.
Waveform: 
Population: 
Data analysis: 
Potential for the unexpected: 
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

18. Gravitational Wave Pulsars
Effective ellipticity of NSs not known, spindown bounds may be weak limits.
Physics involves crust, core.
MS PSRs may reach spindown bound (Cutler).
LIGO data analysis very challenging, a prototype for LISA gravitational capture searches.
Accurate positions (arcsecond) will lead to follow-up observations in radio, X-ray.
Waveform: 
Population: 
Data analysis: 
Potential for the unexpected: 
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

19. Neutron Star Vibrations
r-modes visible in Adv LIGO, may limit spin of LMXBs. Viscosity wipes out r-modes in young stars.
f-, p-modes of NSs excited during formation (hot stars) and probably during glitches, X-ray bursts from magnetars, etc. Need broad-band high-frequency detector to look for these.
Payoff: NS asteroseismology, insight into EOS and other physics
Waveform: 
Population: 
Data analysis: 
Potential for the unexpected: 
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

20. Gravitational Collapse
Numerical simulations needed here as for BH problems. GR hydro codes improving, 3D simulations coming along, bigger computers needed.
Physics probably under control, but initial conditions (esp. rotation) and high-density EOS uncertain.
Pathways to NS or BH, g-bursts, hypernovae: want associated waveforms!
Data analysis for LIGO must be robust, not too dependent on waveform templates, hence sub-optimal. We don’t know how best to do this yet!
Waveform: 
Population: 
Data analysis: 
Potential for the unexpected: 
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources

21. Astrogravs: Overview of GW Sources
Unexpected sources
LISA particularly has high sensitivity, can see some sources w/o filtering, or with short FFTs w no demodulation.
LIGO/GEO/VIRGO may see coincident events of unknown origin.
Search methods in data: many possible methods, no clear performance criteria. Need to run several at once.
30% of the Universe is in matter that can emit no electromagnetic radiation. Is it really so smooth that all the interesting structure and dynamics is in the 4% that carries charge? Only GW observations can answer this!
Waveform: 
Population: 
Data analysis: 
Potential for the unexpected: 
Bernard F Schutz Albert Einstein Institute
24 April 2003
Astrogravs: Overview of GW Sources