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Hier ist mein Bericht fuer das Jahrbuch 2010 der MPG


        GRAVITATIONAL WAVES AND RELAXATION PROCESSES

two supermassive black holes dancing with eachother
When supermassive black holes come to the idea of dancing close to eachother they produce ripples in space-time

Gravity waves?

The theory of general relativity predicts that energy is transmitted in the form of waves across the gravitational field of space-time. Similarly to the electromagnetic theory, when a particle is accelerated it will emit radiation, but in the form of gravity. Laying it on the line, to speak bluntly, gravity will behave as a soup in a plate when something big is passing by... The footsteps of, say, your mother-in-law will make it oscillate and produce small (in the case of the soup) waves. Of course this "mother-in-law approach" should be formulated in terms of the Weyl tensor and the quadrupole.

The Laser Interferometer Space Antenna (LISA) is a spacecraft-based interferometer à la Michelson forming a triangle with arms of five millions kilometers of length, so that it is able to detect displacements produced by the gravitational waves with a resolution of 10 picometer. There is a big expectation to the answers that such a mission could provide us with, for if the existence os the GWs was to be proved, this would be not only an ultimative test for the TGR, but also the answer to loads and loads of questions that, as of now, are impossible to even guess.

Simulating the Nature: Direct N-body methods

The powerful numerical N-body6++ tool has proven to be one of the -if not the- most accurate techniques we have at our disposal nowadays. It has been more than forty years of development and people doing acid tests on it to reach its current state. Why do we rely on it? Basically because we are integrating Newton's equations and, thus, all gravitational Physics just pop up, they are there. In a very short and rough description, we do not make any assumption or approach and "just" compute all gravitational forces between all stars in our system... And that's the reason why we call it "direct" N-body method. Of course there is more pith behind this simple idea.

Special purpose computers for star cluster simulations

As of now, I am developing realistic models to study the merger of two supermassive black holes in a galactic nucleus with the before mentioned tool. A problem we have when trying to simulate what out there exits is the resolution. Our system, our galaxy, has to have a realistic number of stars to reproduce what is happening in the real life, above your head (or below your feet).
two fat lads making space-time go mad
GRAPE board
For this aim, a few years ago, a japanish research group developed special purpose hardware for the numerical code... These computers, called GRAPE, allow you to simulate a huge number of stars that, otherwise, would be impossible to reproduce even with hundreds of normal PCs... They are already talking in terms of petaflops (GRAPE-DR). It is of crucial importance to increase the number of particles we have in the system if we want to study correctly the relaxation. Too few particles lead to the pin-hole regime (full loss-cone), but real galaxies are to have a depleted loss-cone; therefore we have to go to the diffusion situation and, for this, we need at least a number of some millions of stars, even though recent studies show already a diffusion situation for a million particles.

The role of collisional processes

We know that almost all galaxies in the Universe have run, at least, one -if not several- merging process with other galaxies in its lifetime. When two galaxies with a central supermassive black hole collide, the supermassive black holes sink in the new stellar system resulting of the merger to the centre because of dynamical friction. This process dominates the evolution of the system until the interaction with stars coming from the surronding stellar system becomes very important. Slingshot ejections of stars by the black holes binary is the second dominating process to give way (maybe I should say to give in) to the emission of gravitational waves.

Under which circumstances increase or decrease the eccentricity of the binary? Does the geometry of the surronding stellar system lead to a different merging time of the supermassive black holes? And the interaction of it? Plays Brownian motion any role in this scenario at all?

Ongoing work

In order to answer these questions and others, which are fundamental for the detection of massive black holes binaries, I am studying the evolution of equal/different mass ratio supermassive black holes in galactic nuclei. In the figure on your right (click to enlarge) there are some preliminar results on this research.
progress
Orbits of different mass ratio dancing SMBHs in the process of merging (or not?)
After the merger of two galaxies, a supermassive black hole is located in the centre of the resulting core . A second supermassive black hole, but a lighter one, remains in the stellar system orbiting the bigger one (orbit in green). After they "see eachother" they interact and may form a bound system which finally may end up emitting gravitational waves.
One should mention here that, as of now, there exist only Newtonian versions of the standard N-body code. Nonetheless we are developing now a version of it with the 1, 2 and 2.5 postnewtonian terms (relativist corrections to the Newtonian theory) which are responsible for the perihelion shift (1 and 2) and emission of gravitational waves (2.5) and thus be able to study their emission





        DYNAMICS OF DENSE STAR CLUSTERS

Today it is well established that a massive black hole could explain kinematics data in local active and nonactive galaxies. The observed correlation between the MBH s mass and global properties of the spheroidal component of the host galaxy demonstrates that there is an intimate connection between the BH and its host.

A poor star being tidally disrupted by a black hole
A poor star being tidally disrupted by a black hole

There are also indications that this link extends to globular clusters. These are expected to harbour so-called intermediate mass black holes (IMBHs), i.e. BHs whose mass is in the range of 100-10000 solar masses, if one extrapolates these relations to such systems. Recent HST observations of the stellar kinematics at the centre of M15 around the MilkyWay and G1 around M31 have been interpreted as indications of the presence of an IMBH in both clusters.

For the analysis of star clusters with a central BH I employ a so-called anisotropic gaseous model that solves numerically moment equations of the full Fokker-Planck equation with Boltzmann-Vlasov terms on the left- and interaction (collisional) terms on the right-hand side of the equations.
Density evolution in a cluster with an extended mass spectrum (movie)
Density evolution in a cluster with an extended mass spectrum (216K ogg movie)
The cluster is modelled like a self-gravitating, conducting gas sphere. In this method, all quantities of interest are accessible as smooth functions of the radius and time. This enables a detailed study of clean-cut aspects of the dynamics. This model allows us to study the most important physical processes that are present in the evolution of a spherical cluster, like self-gravity, two-body relaxation, stellar evolution, collisions, binary stars etc and, undoubtedly, the interaction with a central BH and the role of a mass spectrum.

For instance, in the figure on your right you have a film on the evolution of the density profiles of different mass groups in a stellar cluster. As times goes on, mass segregation breaks the initial distribution and you can see how the heaviest masses (black dashed curve) sink to the centre and raise the central density, whereas in the outer skirts of the cluster we have a depletion of heavy masses.

Not only did I employ this method, but also the so-called direct N-body technique (see above) to study the dynamics of star clusters. For instace, the dynamical evolution of an isolated self gravitating system with two stellar mass groups is something we address with this code.

Mass segregation in a star cluster
 Mass segregation in a star cluster (courtesy of Marc Freitag)

Clean-cut properties of the cluster dynamics were examined, like core collapse, the evolution of the central potential, as well as escapers. One can improve the statistical significancy of the lower N-simulations by ensemble averages. There are significant deviations of the evolutionary time scale in the regime in which the individual ratio of the heavy to light bodies --> 1. Equipartition slows down the gravothermal contraction of the core slightly. This allows one to study the critical boundary between Spitzer stable and unstable systems.





        The LISA Astro-GR meetings

In September 2006 (18th-22nd) and making an effort to bring together the communities of Astrophysics and General Relativity, I organised a meeting at the Max-Planck Institute for Gravitational Physics (Albert Einstein Institute) which was attended by some 65 people from everywhere (UK, Germany, USA, Russia, China, etc) in order to find out how to work together on the detection of gravitational waves with LISA.

LISA Astro-GR@AEI
Here I am, trying to do the impossible

I guess I should not say it, but everything went fine and some participants even said "it's been the best meeting I've ever been to"; so that I am happy and satisfied. On the right you have one of the pics of th meeting and on the bottom the link to the page, in which you'll find the talks on-line (in the free ogg format, of course) and the slides (in pdf). In the site there is also a list of questions I gathered from many people to be worked out during the satellite discussions.

Another proof that everything was fine is that the meeting had already a continuation, in Como (Italy), in 2008. I organised it with Monica Colpi and Francesco Haardt. Also, later, in the same year, I organised a two-weeks meeting at the AEI following the line of the KITP/Aspen workshops:

http://www.aei.mpg.de/~pau/LISA_Astro-GR@AEI

http://www.aei.mpg.de/~pau/LISA_Astro-GR@Como

http://www.aei.mpg.de/~pau/2W@AEI

--> HERE YOU'LL FIND MORE INFO <--

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Here I try to shortly summarise my current work at the AEI since I started working here. Things are explained in a lousey, informal way, mostly because I want to give -and at the same time have- a global overview of what I am doing.

Therefore I will expand contents step by step, as I progress in the work, to have an idea where I am and try not to lose myself...

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