scott a. hughes, mit gravitation: a decennial...

Scott A. Hughes, MIT Gravitation: A Decennial Perspective

Gravitational waves: tools for studying gravity

Scott A. Hughes, MIT

� Fundamental tests of GR

� Polarizations, graviton mass, speed of gravity, scalar/tensor theories, Lense-Thirring effects

� Window into strong gravity

� Direct observation of nonlinear dynamics of spacetime

� Precision measurement of black hole spacetimes

Gravitation: A Decennial Perspective

Familiar with the potential payoffs to gravity researchthat gravitational-wave measurements will make possible, e.g.:

Obvious why we like this stuff!

Gravitational waves: tools fora new kind of astronomy


Growing realization that this “New window on the universe” is about to open: excitement about gravitational-waves outside of the gravity community running quite high.

What can these observations teach that will be of interest among this broader community?

Focus on the astronomy reach of LISA: what will LISA observations bring to black hole astrophysics?

Argument: Black holes must be ubiquitous


Worth recalling some history:

� Lots of quasars/AGN in the universe. Density particularly high around z = 2, falls off very sharply as we move towards local universe.

� Black hole powered accretion processes are the most reasonable way to explain quasar energetics.

� Inference: massive black holes were common!

� Quasars appear to only be “on” for a relatively short time. Since black holes don't just evaporate (well, not quickly), many (most?) galaxies must be quasar fossils.

� Inference: massive black holes must be everywhere!

Observation: Black holes are ubiquitous!


Finding black holes in quiescent galaxies is quite difficult. Best evidence comes from stellar and/or gas dynamics.

Look nearby, particularly with HST: we see them (almost) everywhere.

More specifically, every galaxy that contains a bulge also contains a black hole, usually with a fairly solid mass estimate. If the galaxy does not contain a bulge (handful of examples), upper limits on the mass of a putative black hole are the best we can do.

Example: M31 (Andromeda)


One of the best studied cases! Nearby, able to do deep, detailed studies.

Kinematics and spectroscopy make a very solid BH detection case.

Example: M87


Another very well studied case: very massive elliptical galaxy in the Virgo cluster with an extremely massive black hole.

Galaxy is essentially one big bulge!

Example: M33


Very nearby galaxy (a few Mpc), great candidate for deep kinematic studies.

No black hole has ever been detected! Consistent with total lack of a bulge.

Bulge properties & black hole properties


Clear trend: big bulge means big black hole.

Even better correlations exist: What's big about the bulges that really matters to an astronomer is their high luminosity:

Clear trend seen ... but quite a bit of scatter among the data.

Would be nice to see a tighter trend, more closelyrelated to physical bulge properties.

The M – σ relation


Particularly nice correlations found with the velocity dispersion σ of the bulge! Scatter is greatly reduced, get a very nice power law.


Plot taken from Gebhardt et al 2000, ApJ, 539, L13.

Connection between bulge and hole


The M – σ relation is particularly compelling because it relates the black hole mass to a fundamental physical property of the bulge.

Worth stressing: The velocity dispersion σ is measured at radii beyond the gravitational influence of the black hole! The black hole should have no influence on the kinematics of the galaxy at those radii ... and yet this is the quantity that most strong correlates with black hole masses.

The growth of galaxies and black holes appears to be fundamentally linked!


What GW observations will bring


Some kind of connection is apparent, but nature of that connection is still rather puzzling: don't have very good ideas about how black holes and bulges grow together, and how the M – σ relation is enforced.

Need new data channels! GWs should allow

� Accurate census

� Of masses: currently most BH masses have rather large error bars on them

� Of spins: we have almost no information about spins today!

� Tracer of primordial mergers.Gravitation: A Decennial Perspective

Census of “local” holes


Extreme mass ratio captures: we usually think of these as the sources that will test the black hole hypothesis, mapping the spacetimes of massive compact objects.

More prosaically, these sources are the tools to use to weigh the black holes of “local” galaxies (within a Gpc or so) to very high accuracy and to measure the spins of those holes.


Keep in mind: currently only know most masses to within a factor of a few. Spins are essentially unknown.

(Barack and Cutler, unpublished)

Measuring spin: capture binaries & GWs


Gravitational capture binaries are formed when a stellar mass compact object is scattered into the “loss cone” of a nuclear black hole:

Zoom:

If the “small” compact body is a 10 solar mass BH, the waves this binary generates can be measured out to about 1 Gpc with high signal-to-noise ratio (~tens – 100 or so) by LISA.

Gravitational capture binaries, pt II


Waves generated by these binaries are in the LISA band if the large hole has a mass of around 1 million solar masses.

Binary circularizes and shrinks due to backreaction of gravitational waves:

Last 100,000 or so orbits generate waves from the extremely deep strong field, in LISA's sensitive band.


Character of deep strong field waves


The waves are generated as the smaller member of the binary orbits deep in the potential well of the large hole – imprint of general relativity on these orbits is very strong.

Extremely non-Newtonian character! Waves are “colored” by 3 orbital frequencies:

Differences between these three frequencies encode properties of the strong field nature of black hole spacetime – particularly spin.


Imprint of spin on frequenciesThe difference between the azimuthal and the radial frequencies is well known to us: it causes the perihelion precession of Mercury.

Effects are quite a bit more pronounced for black hole orbits! “Extra” precessional angle can be thousands of radians per orbit – much larger due to strong gravitational fields and intense spin-induced frame dragging.

The difference between the azimuthal and the radial frequencies is well known to us: it causes the perihelion precession of Mercury.


Spin parameter a = 0.998


Imprint of frequencies on GWs


These frequencies are directly imprinted on the gravitational wave: roughly speaking, we see a carrier wave with very strong modulations. The modulations come from the extra “precessional” effects and encode information such as spin.

Example: snapshots of the gravitational waves generated by highly eccentric inspiral.

Harmonics of the phi and r frequencies influence this waveform.





Example: snapshots of the gravitational waves generated by quasi-circular inspiral.

Harmonics of the phi and theta frequencies influence this waveform.





It is this strong imprint of spin upon these waves that makes it possible to measure that spin so accurately!


What good are spin measurements?


Suggests that a rapidly rotating hole cannot haverecently undergone a merger with another black hole:recent growth is most likely due to accretion.

Measuring the mass and spin of holes tells us about their recent growth history. Spin is a particularly powerful discriminant:

� Accretion tends to make holes spin faster

� Mergers tend to make holes spin slower.


Why do mergers spin holes down???


Binary with mass ratio q forms following galaxy merger or by capture in the nucleus of a galaxy. When gravitational-wave emission becomes significant, binary shrinks due to radiative loss of energy and angular momentum.

Shrinks until smaller member of the binary reaches the last stable orbit and plunges into the larger hole. Orbital constants are carried into the larger hole. In particular, orbital angular momentum adds to the spin:


Doctrine of Original Spin


At leading order, the net effect washes out: end up with the vectorial spin remaining constant while the mass grows. The spin parameter and rotation frequency decrease:

If a black hole repeatedly suffers mergers and the orbital orientation of these mergers is randomly distributed, get just as many aligned mergers as anti-aligned mergers.

(Hughes and Blandford 2003, ApJ, 585, L101)


Doctrine of Original Spin: Reformation


Magnitude of the orbital angular momentum at plunge varies very strongly as a function of the alignment between spin and orbit ...

Under multiple mergers, black hole spin decreases even faster than the Doctrine predicts:

Smallest magnitude for spin and orbit parallel ...Largest magnitude for spin and orbit antiparallel!


Mortal Spin trumps Original Spin


If orbital angular momentum overwhelms spin, this goes out the window! Spin of the merged remnant is then dominated by orbital angular momentum at plunge. This “mortal spin” can be large, leaving a rapidly rotating remnant.

For this to happen, must have


which translates to a fairly severe constraint on the mass ratio of the binary:

Requires relatively rare events for mergers to leave a rapidly rotating remnant.

Contrast: accretion driven growth


Accretion spins holes up! Even if a disk is aligned the “wrong way” (i.e., against the hole's spin), it doesn't take long for the hole to be spun up parallel to the disk's orientation. Expect spin to be fairly rapid:

Thin disk accretion with buffering by retrograde photon capture from a hot photosphere: a/M = 0.998 (Thorne 1974, ApJ 191, 507).

Thick disk accretion with buffering from magnetic coupling between horizon and plasma: 0.6 < a/M < 0.9 (e.g., Moderski et al 1998, MNRAS 301, 142).

A lot to learn by measuring the spin!Gravitation: A Decennial Perspective

Formation of black holes and structure


Some of greatest excitement comes from the potential of LISA to probe the origins and evolution of massive black holes.

Reach is enormous! Mergers related to the formation of the first structures can be probed.

Hierarchical structure formation


Earliest structures are essentially just dark matter “halos” – spheroidal, gravitating globs of dark matter with a few bits of gunk (baryons) coming along for the ride – seeded by overdensities in the primordial matter field with largest magnitude.

These haloes fall into one another, merging repeatedly. Merging halos grow into galaxies.

Black holes will form inside some of the halos, be carried along and merge with other black holes when their halos merge. BBH mergers are a natural consequence of hierarchical structure formation!


Action shot: mergers at high redshift


Mergers in rich cluster MS 1054-03 (z = 0.83). Shown: 16 brightest galaxies. About 20% are merging!


van Dokkum et al 1999, ApJ 520, L95

Inaction shot: no mergers at low redshift


Essentially no mergers seen in MS 1358-62 (z = 0.32). Shown: 16 brightest galaxies. No mergers apparent here!


van Dokkum et al 1999, ApJ 520, L95

The universe liked to merge galaxies at high redshift! Likely that black hole mergers were more common as well


LISA is likely to see most of its mergers at high redshift – tool for detangling the mergers of early structures. (Note added “in press”: see astro-ph/0306105 for even more high redshift galaxy mergers!)

To get the really interesting information, want to measure masses and redshifts of merging black holes.

Masses and merger rates as function of redshift will teach us a lot (e.g., Menou, Haiman, Narayanan 2001, ApJ 558, 535).

Mass-redshift degeneracy


The waves directly encode information about masses and distance: for a “local” binary

Cosmology happens: need to redshift all of the masses (from redshifting of dynamical timescales), change r into a luminosity distance:


Use cosmographic knowledge...


We now know the geometry of our universe well enough that we can, with decent accuracy turn what LISA measures around and infer the redshift.

Our universe is cosmological constant dominated (70%) with clumpy matter making up the rest (30%), and with a Hubble constant 70 (km/sec)/Mpc. These statements are true with about 10% accuracy.

Standard formulae allow us to plug in these values and map our measured D to an inferred redshift z (with error ~10%). We can thus map the mass of typical mergers with 10%(ish) accuracy!


Works pretty well!


� Luminosity distance: most likely measurement has error less than 5%; most points are inside 20%.

� Error in redshift due to uncertainty in cosmology, not measurement error.

� Redshifted mass determinations are phenomenal!

Results for

Salient details:


Higher redshift: still good


Results for At high redshift, some degradation in parameter measurement accuracy – but still quite good!

Typical distance measurement error is tens of percent; inverting for redshift get similar magnitude of error.

Redshifted mass determination about as accurate as at lower redshift.


Summary: broad trends


� Masses of the system are best measured when the total redshifted mass of the binary black hole lies in the range .

� Still get information outside this range, just not quite as pretty.

� Distance is determined quite accurately (5 – 20% error) provided we get a few months of inspiral.

� Rough rule of thumb: LISA must move through a radian of orbit.

� In most cases, redshift error is dominated by present errors in cosmological parameters. Will get better as we pin down the cosmology better!


What if we could associate a counterpart with the GW event?


Pointing accuracy of any “electromagnetic telescope” is likely to be far better than what LISA can do. Independent position determination breaks a lot of degeneracies among parameters – could vastly improve distance determination!

Peak error in distance in this case is around 0.1%.

Can imagine getting redshift and distance – standard candle!



Great gravity ... and great astronomy!


Information and data from LISA will be of interest to a very broad community: ability to probe properties and evolution of black holes will impact a lot of scientific programs. The next 10 years will see astronomers welcoming us with open arms!

Aidan Hughes, “Prodigal Son”, www.bruteprop.com/gallery

scott a. hughes, mit gravitation: a decennial...

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